Alpha factor mining is pivotal in quantitative investment for identifying predictive signals from complex financial data. While traditional formulaic alpha mining relies on human expertise, contemporary automated methods, such as those based on genetic programming or reinforcement learning, often struggle with search inefficiency or yield alpha factors that are difficult to interpret. This paper introduces a novel framework that integrates Large Language Models (LLMs) with Monte Carlo Tree Search (MCTS) to overcome these limitations. Our framework leverages the LLM's instruction-following and reasoning capability to iteratively generate and refine symbolic alpha formulas within an MCTS-driven exploration. A key innovation is the guidance of MCTS exploration by rich, quantitative feedback from financial backtesting of each candidate factor, enabling efficient navigation of the vast search space. Furthermore, a frequent subtree avoidance mechanism is introduced to enhance search diversity and prevent formulaic homogenization, further improving performance. Experimental results on real-world stock market data demonstrate that our LLM-based framework outperforms existing methods by mining alphas with superior predictive accuracy and trading performance. The resulting formulas are also more amenable to human interpretation, establishing a more effective and efficient paradigm for formulaic alpha mining.

As a fundamental method in economics and finance, the factor model has been extensively utilized in quantitative investment. In recent years, there has been a paradigm shift from traditional linear models with expert-designed factors to more flexible nonlinear machine learning-based models with data-driven factors, aiming to enhance the effectiveness of these factor models. However, due to the low signal-to-noise ratio in market data, mining effective factors in data-driven models remains challenging. In this work, we propose a hypergraph-based factor model with temporal residual contrastive learning (FactorGCL) that employs a hypergraph structure to better capture high-order nonlinear relationships among stock returns and factors. To mine hidden factors that supplement human-designed prior factors for predicting stock returns, we design a cascading residual hypergraph architecture, in which the hidden factors are extracted from the residual information after removing the influence of prior factors. Additionally, we propose a temporal residual contrastive learning method to guide the extraction of effective and comprehensive hidden factors by contrasting stock-specific residual information over different time periods. Our extensive experiments on real stock market data demonstrate that FactorGCL not only outperforms existing state-of-the-art methods but also mines effective hidden factors for predicting stock returns.

In this paper, we study the stochastic probing problem under a general monotone norm objective. We are given a ground set $U=[n]=\{1,2, \ldots, n\}$, where each element i is associated with an independent nonnegative random variable $X_{i}$ (with a known distribution). We may probe these elements adaptively, and upon probing an element i, its value $X_{i}$ is realized. The sequence of probed elements must satisfy a prefix-closed feasibility constraint $\mathcal{F}$, such as a matroid, an orienteering constraint, or any other downward-closed constraint. We also have a monotone norm function $f: \mathbb{R}_{\geq 0}^{n} \rightarrow \mathbb{R}_{\geq 0}$. Let $P \subseteq U$ be the set of probed elements. Then the reward is $f\left(X_{P}\right)$, where $X_{P}$ is an n-dimensional vector whose i-th coordinate equals the realized value of $X_{i}$ if $i \in P$ (i.e., element i is probed), and 0 otherwise. Our objective is to design a probing strategy that maximizes the expected reward $\mathbb{E}\left[f\left(X_{P}\right)\right]$. We study the adaptivity gap of the problem, defined as the ratio between the expected reward of an optimal adaptive strategy and that of an optimal non-adaptive strategy. A small adaptivity gap allows us to focus on designing nonadaptive strategies, which are typically simpler to represent and analyze. Establishing tight adaptivity gaps is a central challenge in stochastic combinatorial optimization and has been studied extensively for stochastic probing problems with various objective functions. In this paper, we resolve a central open problem in this line of research, posed in [1], [2], by proving that the adaptivity gap for stochastic probing with general monotone norms is bounded by $O\left(\log ^{2} n\right)$. With a refined analysis, we can further strengthen the bound to $O(\log r \log n / \log \log n)$ where r is the maximum length of a sequence in the feasibility constraint ($2 \leq r \leq n$). As a by-product, we obtain an asymptotically tight adaptivity gap $\Theta(\log n / \log \log n)$ for Bernoulli stochastic probing with binary-XOS objectives, matching the lower bound in [1]. We also obtain an $O\left(\log ^{3} n\right)$ upper bound for Bernoulli stochastic probing with general subadditive objectives. Furthermore, for monotone symmetric norms, we prove that the adaptivity gap can be bounded by $O(1)$, answering an open question posed in [3] and improving upon their $O(\log n)$ upper bound. Index Terms-stochastic probing, adaptivity gap, subadditive objective

Designing small-sized coresets, which approximately preserve the costs of the solutions for large datasets, has been an important research direction for the past decade. We consider coreset construction for a variety of general constrained clustering problems. We introduce a general class of assignment constraints, including capacity constraints on cluster centers, and assignment structure constraints for data points (modeled by a convex body B ). We give coresets for clustering problems with such general assignment constraints that significantly generalize and improve known results. Notable implications include the first ε-coreset for capacitated and fair k-MEDIAN with m outliers in Euclidean spaces whose size is Õ (m + k2ε-4), generalizing and improving upon the prior bounds in [BCJ+ 22, HJLW23] (for capacitated k-MEDIAN, the coreset size bound obtained in [BCJ+22] is Õ (k3ε-6), and for k-MEDIAN with m outliers, the coreset size bound obtained in [HJLW23] is Õ (m + k3ε-5)), and the first ε-coreset of size poly(kε-1) for fault-tolerant clustering for various types of metric spaces.

Time series forecasting is one of the most important procedures within various real-world machine learning applications. However, the complexity and non-stationary nature of many realistic time series data challenges people to make reliable predictions. In this paper, we propose a novel Causal Stacking Hidden Markov model termed CASH to make reliable predictions while mining effective hidden states. CASH leverages structural invariances of causal inference and efficient hidden state uncovering capability of the Hidden Markov Model (HMM). It attributes time series signal movements to short-term, medium-term, and long-term factors, taking into account all three by stacking HMMs in-depth and enhanced by an attention mechanism. Subsequently, utilizing a reformulated sequential variational auto-encoder objective function, CASH learns effective hidden states in an unsupervised manner. For the final prediction, the hidden states are processed in a temporal attention layer to leverage labels. Comprehensive experiments on three realistic financial datasets and twenty multivariate time series classification datasets demonstrate the proposed CASH outperforms the state-of-the-art benchmarks on most datasets.

Constructing small-sized coresets for various clustering problems in different metric spaces has attracted significant attention for the past decade. A central problem in the coreset literature is to understand what is the best possible coreset size for (k,z)-clustering in Euclidean space. While there has been significant progress in the problem, there is still a gap between the state-of-the-art upper and lower bounds. For instance, the best known upper bound for k-means (z=2) is min{O(k3/2 ε−2),O(k ε−4)} [Cohen-Addad, Larsen, Saulpic, Schwiegelshohn, Sheikh-Omar, NeurIPS’22], while the best known lower bound is Ω(kε−2) [Cohen-Addad, Larsen, Saulpic, Schwiegelshohn. STOC’22]. In this paper, we make significant progress on both upper and lower bounds. For a large range of parameters (i.e., ε, k), we have a complete understanding of the optimal coreset size. In particular, we obtain the following results: (1) We present a new coreset lower bound Ω(k ε−z−2) for Euclidean (k,z)-clustering when ε ≥ Ω(k−1/(z+2)). In view of the prior upper bound Õz(k ε−z−2) [Cohen-Addad, Larsen, Saulpic, Schwiegelshohn. STOC’22], the bound is optimal. The new lower bound is surprising since Ω(kε−2) [Cohen-Addad, Larsen, Saulpic, Schwiegelshohn. STOC’22] is “conjectured” to be the correct bound in some recent works (see e.g., [Cohen-Addad, Larsen, Saulpic, Schwiegelshohn. STOC’22; Cohen-Addad, Larsen, Saulpic, Schwiegelshohn, Sheikh-Omar, NeurIPS’22]). Our new lower bound instance is a delicate construction with multiple clusters of points, which is a significant departure from the previous construction in [Cohen-Addad, Larsen, Saulpic, Schwiegelshohn. STOC’22] that contains a single cluster of points. The new lower bound also implies improved lower bounds for (k,z)-clustering in doubling metrics. (2) For the upper bound, we provide efficient coreset construction algorithms for (k,z)-clustering with improved or optimal coreset sizes in several metric spaces. In particular, we provide an Õz(k2z+2/z+2 ε−2)-sized coreset, with a unfied analysis, for (k,z)-clustering for all z≥ 1 in Euclidean space. This upper bound improves upon the Õz(k2ε−2) upper bound by [Cohen-Addad, Larsen, Saulpic, Schwiegelshohn. STOC’22] (when k≤ ε−1), and matches the recent independent results [Cohen-Addad, Larsen, Saulpic, Schwiegelshohn, Sheikh-Omar, NeurIPS’22] for k-median and k-means (z=1,2) and extends them to all z≥ 1.

Feature importance scores (FIS) estimation is an important problem in many data-intensive applications. Traditional approaches can be divided into two types; model-specific methods and model-agnostic methods. In this work, we present FeatureLTE, a novel learning-based approach to FIS estimation. For the first time, as we demonstrate through extensive experiments, it is possible to build general-purpose pre-trained models for FIS estimation. Therefore, FIS estimation reduces to prediction outputs from a pre-trained FeatureLTE model. Pre-trained FeatureLTE models enjoy several desired advantages, including accuracy, robustness, efficiency, and evolvability, and FeatureLTE models really begin to shine on large datasets where traditional methods often find themselves unable to scale. We build our pre-trained models for binary classification and regression problems using observations from nearly 1,000 public datasets. We systematically evaluate various design choices of FeatureLTE model construction and carefully design meta features to make sure that they are computationally lightweight. Based on our evaluation, FeatureLTE is on par with the best existing FIS estimators in terms of FIS quality, and achieves up to 339.48x speedup without sacrificing the quality of FIS estimates on large-scale datasets. Finally, we release two pre-trained FeatureLTE models for binary classification and regression problems that are ready to use on almost all tabular datasets, along with the repository of 701 binary classification datasets and 256 regression datasets with pre-computed feature importance scores to promote future research along this direction.

Graph contrastive learning (GCL) has attracted a surge of attention due to its superior performance for learning node/graph representations without labels. However, in practice, the underlying class distribution of unlabeled nodes for the given graph is usually imbalanced. This highly imbalanced class distribution inevitably deteriorates the quality of learned node representations in GCL. Indeed, we empirically find that most state-of-the-art GCL methods cannot obtain discriminative representations and exhibit poor performance on imbalanced node classification. Motivated by this observation, we propose a principled GCL framework on Imbalanced node classification (ImGCL), which automatically and adaptively balances the representations learned from GCL without labels. Specifically, we first introduce the online clustering based progressively balanced sampling (PBS) method with theoretical rationale, which balances the training sets based on pseudo-labels obtained from learned representations in GCL. We then develop the node centrality based PBS method to better preserve the intrinsic structure of graphs, by upweighting the important nodes of the given graph. Extensive experiments on multiple imbalanced graph datasets and imbalanced settings demonstrate the effectiveness of our proposed framework, which significantly improves the performance of the recent state-of-the-art GCL methods. Further experimental ablations and analyses show that the ImGCL framework consistently improves the representation quality of nodes in under-represented (tail) classes.

Large-scale high-quality data is critical for training modern deep neural networks. However, data acquisition can be costly or time-consuming for many time-series applications, thus researchers turn to generative models for generating synthetic time-series data. In particular, recent generative adversarial networks (GANs) have achieved remarkable success in time-series generation. Despite their success, existing GAN models typically generate the sequences in an auto-regressive manner, and we empirically observe that they suffer from severe distribution shifts and bias amplification, especially when generating long sequences. To resolve this problem, we propose Adversarial Error Correction GAN (AEC-GAN), which is capable of dynamically correcting the bias in the past generated data to alleviate the risk of distribution shifts and thus can generate high-quality long sequences. AEC-GAN contains two main innovations: (1) We develop an error correction module to mitigate the bias. In the training phase, we adversarially perturb the realistic time-series data and then optimize this module to reconstruct the original data. In the generation phase, this module can act as an efficient regulator to detect and mitigate the bias. (2) We propose an augmentation method to facilitate GAN's training by introducing adversarial examples. Thus, AEC-GAN can generate high-quality sequences of arbitrary lengths, and the synthetic data can be readily applied to downstream tasks to boost their performance. We conduct extensive experiments on six widely used datasets and three state-of-the-art time-series forecasting models to evaluate the quality of our synthetic time-series data in different lengths and downstream tasks. Both the qualitative and quantitative experimental results demonstrate the superior performance of AEC-GAN over other deep generative models for time-series generation.

Graph Neural Networks (GNNs) have already been widely used in various graph mining tasks. However, recent works reveal that the learned weights (channels) in well-trained GNNs are highly redundant, which inevitably limits the performance of GNNs. Instead of removing these redundant channels for efficiency consideration, we aim to reactivate them to enlarge the representation capacity of GNNs for effective graph learning. In this paper, we propose to substitute these redundant channels with other informative channels to achieve this goal. We introduce a novel GNN learning framework named AKE-GNN, which performs the Adaptive Knowledge Exchange strategy among multiple graph views generated by graph augmentations. AKE-GNN first trains multiple GNNs each corresponding to one graph view to obtain informative channels. Then, AKE-GNN iteratively exchanges redundant channels in the weight parameter matrix of one GNN with informative channels of another GNN in a layer-wise manner. Additionally, existing GNNs can be seamlessly incorporated into our framework. AKE-GNN achieves superior performance compared with various baselines across a suite of experiments on node classification, link prediction, and graph classification. In particular, we conduct a series of experiments on 15 public benchmark datasets, 8 popular GNN models, and 3 graph tasks and show that AKE-GNN consistently outperforms existing popular GNN models and even their ensembles. Extensive ablation studies and analyses on knowledge exchange methods validate the effectiveness of AKE-GNN.

Optimized trade execution is to sell (or buy) a given amount of assets in a given time with the lowest possible trading cost. Recently, reinforcement learning (RL) has been applied to optimized trade execution to learn smarter policies from market data. However, we find that many existing RL methods exhibit considerable overfitting which prevents them from real deployment. In this paper, we provide an extensive study on the overfitting problem in optimized trade execution. First, we model the optimized trade execution as offline RL with dynamic context (ORDC), where the context represents market variables that cannot be influenced by the trading policy and are collected in an offline manner. Under this framework, we derive the generalization bound and find that the overfitting issue is caused by large context space and limited context samples in the offline setting. Accordingly, we propose to learn compact representations for context to address the overfitting problem, either by leveraging prior knowledge or in an end-to-end manner. To evaluate our algorithms, we also implement a carefully designed simulator based on historical limit order book (LOB) data to provide a high-fidelity benchmark for different algorithms. Our experiments on the high-fidelity simulator demonstrate that our algorithms can effectively alleviate overfitting and achieve better performance.

We study the generalized load-balancing (GLB) problem, where we are given n jobs, each of which needs to be assigned to one of m unrelated machines with processing times {pij}. Under a job assignment σ, the load of each machine i is Ψi(pi[σ]) where ψi: ℝn → ℝ≥0 is a symmetric monotone norm and pi[σ] is the n- dimensional vector {pij ·

As an asset pricing model in economics and finance, factor model has been widely used in quantitative investment. Towards building more effective factor models, recent years have witnessed the paradigm shift from linear models to more flexible nonlinear data-driven machine learning models. However, due to low signal-to-noise ratio of the financial data, it is quite challenging to learn effective factor models. In this paper, we propose a novel factor model, FactorVAE, as a probabilistic model with inherent randomness for noise modeling. Essentially, our model integrates the dynamic factor model (DFM) with the variational autoencoder (VAE) in machine learning, and we propose a prior-posterior learning method based on VAE, which can effectively guide the learning of model by approximating an optimal posterior factor model with future information. Particularly, considering that risk modeling is important for the noisy stock data, FactorVAE can estimate the variances from the distribution over the latent space of VAE, in addition to predicting returns. The experiments on the real stock market data demonstrate the effectiveness of FactorVAE, which outperforms various baseline methods.

Portfolio management is a fundamental problem in finance. It involves periodic reallocations of assets to maximize the expected returns within an appropriate level of risk exposure. Deep reinforcement learning (RL) has been considered a promising approach to solving this problem owing to its strong capability in sequential decision making. However, due to the non-stationary nature of financial markets, applying RL techniques to portfolio optimization remains a challenging problem. Extracting trading knowledge from various expert strategies could be helpful for agents to accommodate the changing markets. In this paper, we propose MetaTrader, a novel two-stage RL-based approach for portfolio management, which learns to integrate diverse trading policies to adapt to various market conditions. In the first stage, MetaTrader incorporates an imitation learning objective into the reinforcement learning framework. Through imitating different expert demonstrations, MetaTrader acquires a set of trading policies with great diversity. In the second stage, MetaTrader learns a meta-policy to recognize the market conditions and decide on the most proper learned policy to follow. We evaluate the proposed approach on three real-world index datasets and compare it to state-of-the-art baselines. The empirical results demonstrate that MetaTrader significantly outperforms those baselines in balancing profits and risks. Furthermore, thorough ablation studies validate the effectiveness of the components in the proposed approach.

Reinforcement learning (RL) techniques have shown great success in many challenging quantitative trading tasks, such as portfolio management and algorithmic trading. Especially, intraday trading is one of the most profitable and risky tasks because of the intraday behaviors of the financial market that reflect billions of rapidly fluctuating capitals. However, a vast majority of existing RL methods focus on the relatively low frequency trading scenarios (e.g., day-level) and fail to capture the fleeting intraday investment opportunities due to two major challenges: 1) how to effectively train profitable RL agents for intraday investment decision-making, which involves high-dimensional fine-grained action space; 2) how to learn meaningful multi-modality market representation to understand the intraday behaviors of the financial market at tick-level.

Entity resolution (ER) is a core problem in data integration. Many companies have lots of datasets where ER needs to be conducted to integrate the data. On the one hand, it is nontrivial for non-ER experts within companies to design ER solutions. On the other hand, most companies are reluctant to release their real datasets for multiple reasons (e.g., privacy issues). A typical solution from the machine learning (ML) and the statistical community is to create surrogate (a.k.a. analogous) datasets based on the real dataset, release these surrogate datasets to the public to train ML models, such that these models trained on surrogate datasets can be either directly used or be adapted for the real dataset by the companies. In this paper, we study a new problem of synthesizing surrogate ER datasets using transformer models, with the goal that the ER model trained on the synthesized dataset can be used directly on the real dataset. We propose privacy preserving methods to synthesize ER datasets: we first learn the true similarity distributions of both matching and non-matching entity pairs from real dataset. We then devise algorithms that satisfy differential privacy and can synthesize fake but semantically meaningful entities, add matching and non-matching labels to these fake entity pairs, and ensure that the fake and real datasets have similar distributions. We also describe a method for entity rejection to avoid synthesizing bad fake entities that may destroy the original distributions. Extensive experiments show that ER matchers trained on real and synthetic ER datasets have very close performance on the same test sets - their$F1$scores differ within 6% on 3 commonly used ER datasets, and their average precision, recall differences are less than 5%.

Graph Neural Networks (GNNs) have become increasingly popular and achieved impressive results in many graph-based applications. However, extensive manual work and domain knowledge are required to design effective architectures, and the results of GNN models have high variance with different training setups, which limits the application of existing GNN models. In this paper, we present AutoHEnsGNN, a framework to build effective and robust models for graph tasks without any human intervention. AutoHEnsGNN won first place in the AutoGraph Challenge for KDD Cup 2020, and achieved the best rank score of five real-life datasets in the final phase. Given a task, AutoHEnsGNN first applies a fast proxy evaluation to automatically select a pool of promising GNN models. Then it builds a hierarchical ensemble framework: 1) We propose graph self-ensemble (GSE), which can reduce the variance of weight initialization and efficiently exploit the information of local and global neighborhoods; 2) Based on GSE, a weighted ensemble of different types of GNN models is used to effectively learn more discriminative node representations. To efficiently search the architectures and ensemble weights, we propose AutoHEnsGNNGradient, which treats the architectures and ensemble weights as architecture parameters and uses gradient-based architecture search to obtain optimal configurations, and AutoHEnsGNNAdaptive, which can adaptively adjust the ensemble weight based on the model accuracy. Extensive experiments on node classification, graph classification, edge prediction and KDD Cup challenge demonstrate the effectiveness and generality of AutoHEnsGNN.

Weight sharing is a popular approach to reduce the training cost of neural architecture search (NAS) by reusing the weights of shared operators from previously trained child models. However, the rank correlation between the estimated accuracy and ground truth accuracy of those child models is low due to the interference among different child models caused by weight sharing. In this paper, we investigate the interference issue by sampling different child models and calculating the gradient similarity of shared operators, and observe that: 1) the interference on a shared operator between two child models is positively correlated with the number of different operators between them; 2) the interference is smaller when the inputs and outputs of the shared operator are more similar. Inspired by these two observations, we propose two approaches to mitigate the interference: 1) rather than randomly sampling child models for optimization, we propose a gradual modification scheme by modifying one operator between adjacent optimization steps to minimize the interference on the shared operators; 2) forcing the inputs and outputs of the operator across all child models to be similar to reduce the interference. Experiments on a BERT search space verify that mitigating interference via each of our proposed methods improves the rank correlation of super-pet and combining both methods can achieve better results. Our discovered architecture outperforms RoBERTa$_{\rm base}$ by 1.1 and 0.6 points and ELECTRA$_{\rm base}$ by 1.6 and 1.1 points on the dev and test set of GLUE benchmark. Extensive results on the BERT compression, reading comprehension and large-scale image classification tasks also demonstrate the effectiveness and generality of our proposed methods.

While large-scale neural language models, such as GPT2 and BART,have achieved impressive results on various text generation tasks, they tend to get stuck in undesirable sentence-level loops with maximization-based decoding algorithms (\textit{e.g.}, greedy search). This phenomenon is counter-intuitive since there are few consecutive sentence-level repetitions in the human corpus (e.g., 0.02\% in Wikitext-103). To investigate the underlying reasons for generating consecutive sentence-level repetitions, we study the relationship between the probability of repetitive tokens and their previous repetitions in context. Through our quantitative experiments, we find that 1) Models have a preference to repeat the previous sentence; 2) The sentence-level repetitions have a \textit{self-reinforcement effect}: the more times a sentence is repeated in the context, the higher the probability of continuing to generate that sentence; 3) The sentences with higher initial probabilities usually have a stronger self-reinforcement effect. Motivated by our findings, we propose a simple and effective training method \textbf{DITTO} (Pseu\underline{D}o-Repet\underline{IT}ion Penaliza\underline{T}i\underline{O}n), where the model learns to penalize probabilities of sentence-level repetitions from synthetic repetitive data. Although our method is motivated by mitigating repetitions, our experiments show that DITTO not only mitigates the repetition issue without sacrificing perplexity, but also achieves better generation quality. Extensive experiments on open-ended text generation (Wikitext-103) and text summarization (CNN/DailyMail) demonstrate the generality and effectiveness of our method.

We study a general Markov game with metric switching costs: in each round, the player adaptively chooses one of several Markov chains to advance with the objective of minimizing the expected cost for at least k chains to reach their target states. If the player decides to play a different chain, an additional switching cost is incurred. The special case in which there is no switching cost was solved optimally by Dumitriu, Tetali and Winkler [DTW03] by a variant of the celebrated Gittins Index for the classical multi-armed bandit (MAB) problem with Markovian rewards [Git74, Git79]. However, for Markovian multi-armed bandit with nontrivial switching cost, even if the switching cost is a constant, the classic paper by Banks and Sundaram [BS94] showed that no index strategy can be optimal.1 In this paper, we complement their result and show there is a simple index strategy that achieves a constant approximation factor if the switching cost is constant and k = 1. To the best of our knowledge, this index strategy is the first strategy that achieves a constant approximation factor for a general Markovian MAB variant with switching costs. For the general metric, we propose a more involved constant-factor approximation algorithm, via a nontrivial reduction to the stochastic k-TSP problem, in which a Markov chain is approximated by a random variable. Our analysis makes extensive use of various interesting properties of the Gittins index.

We study two generalizations of classic clustering problems called dynamic ordered k-median and dynamic k-supplier, where the points that need clustering evolve over time, and we are allowed to move the cluster centers between consecutive time steps. In these dynamic clustering problems, the general goal is to minimize certain combinations of the service cost of points and the movement cost of centers, or to minimize one subject to some constraints on the other. We obtain a constant-factor approximation algorithm for dynamic ordered k-median under mild assumptions on the input. We give a 3-approximation for dynamic k-supplier and a multi-criteria approximation for its outlier version where some points can be discarded, when the number of time steps is two. We complement the algorithms with almost matching hardness results.

We propose and analyze several stochastic gradient algorithms for finding stationary points or local minimum in nonconvex, possibly with nonsmooth regularizer, finite-sum and online optimization problems. First, we propose a simple proximal stochastic gradient algorithm based on variance reduction called ProxSVRG+. We provide a clean and tight analysis of ProxSVRG+, which shows that it outperforms the deterministic proximal gradient descent (ProxGD) for a wide range of minibatch sizes, hence solves an open problem proposed in Reddi et al. 2016. Also, ProxSVRG+ uses much less proximal oracle calls than ProxSVRG (Reddi et al. 2016) and extends to the online setting by avoiding full gradient computations. Then, we further propose an optimal algorithm, called SSRGD, based on ARAH (Nguyen et al. 2017) and show that SSRGD further improves the gradient complexity of ProxSVRG+ and achieves the the optimal upper bound, matching the known lower bound. Moreover, we show that both ProxSVRG+ and SSRGD enjoy automatic adaptation with local structure of the objective function such as the Polyak-Lojasiewicz (PL) condition for nonconvex functions in the finite-sum case, i.e., we prove that both of them can automatically switch to faster global linear convergence without any restart performed in prior work. Finally, we focus on the more challenging problem of finding an $(\epsilon, \delta)$-local minimum instead of just finding an $\epsilon$-approximate (first-order) stationary point (which may be some bad unstable saddle points). We show that SSRGD can find an $(\epsilon, \delta)$-local minimum by simply adding some random perturbations. Our algorithm is almost as simple as its counterpart for finding stationary points, and achieves similar optimal rates.

Exploration is essential for reinforcement learning (RL). To face the challenges of exploration, we consider a reward-free RL framework that completely separates exploration from exploitation and brings new challenges for exploration algorithms. In the exploration phase, the agent learns an exploratory policy by interacting with a reward-free environment and collects a dataset of transitions by executing the policy. In the planning phase, the agent computes a good policy for any reward function based on the dataset without further interacting with the environment. This framework is suitable for the meta RL setting where there are many reward functions of interest. In the exploration phase, we propose to maximize the Renyi entropy over the state-action space and justify this objective theoretically. The success of using Renyi entropy as the objective results from its encouragement to explore the hard-to-reach state-actions. We further deduce a policy gradient formulation for this objective and design a practical exploration algorithm that can deal with complex environments. In the planning phase, we solve for good policies given arbitrary reward functions using a batch RL algorithm. Empirically, we show that our exploration algorithm is effective and sample efficient, and results in superior policies for arbitrary reward functions in the planning phase.

While pre-trained language models (e.g., BERT) have achieved impressive results on different natural language processing tasks, they have large numbers of parameters and suffer from big computational and memory costs, which make them difficult for real-world deployment. Therefore, model compression is necessary to reduce the computation and memory cost of pre-trained models. In this work, we aim to compress BERT and address the following two challenging practical issues: (1) The compression algorithm should be able to output multiple compressed models with different sizes and latencies, in order to support devices with different memory and latency limitations; (2) The algorithm should be downstream task agnostic, so that the compressed models are generally applicable for different downstream tasks. We leverage techniques in neural architecture search (NAS) and propose NAS-BERT, an efficient method for BERT compression. NAS-BERT trains a big supernet on a carefully designed search space containing a variety of architectures and outputs multiple compressed models with adaptive sizes and latency. Furthermore, the training of NAS-BERT is conducted on standard self-supervised pre-training tasks (e.g., masked language model) and does not depend on specific downstream tasks. Thus, the compressed models can be used across various downstream tasks. The technical challenge of NAS-BERT is that training a big supernet on the pre-training task is extremely costly. We employ several techniques including block-wise search, search space pruning, and performance approximation to improve search efficiency and accuracy. Extensive experiments on GLUE and SQuAD benchmark datasets demonstrate that NAS-BERT can find lightweight models with better accuracy than previous approaches, and can be directly applied to different downstream tasks with adaptive model sizes for different requirements of memory or latency.

It is known that existing policy gradient methods (such as vanilla policy gradient, PPO, A2C) may suffer from overly large gradients when the current policy is close to deterministic, leading to an unstable training process. We show that such instability can happen even in a very simple environment. To address this issue, we propose a new method, called target distribution learning (TDL), for policy improvement in reinforcement learning. TDL alternates between proposing a target distribution and training the policy network to approach the target distribution. TDL is more effective in constraining the KL divergence between updated policies, and hence leads to more stable policy improvements over iterations. Our experiments show that TDL algorithms perform comparably to (or better than) state-of-the-art algorithms for most continuous control tasks in the MuJoCo environment while being more stable in training.

\emph{Anderson acceleration} (or Anderson mixing) is an efficient acceleration method for fixed point iterations $x_{t+1}=G(x_t)$, e.g., gradient descent can be viewed as iteratively applying the operation $G(x) \triangleq x-\alphaabla f(x)$. It is known that Anderson acceleration is quite efficient in practice and can be viewed as an extension of Krylov subspace methods for nonlinear problems. In this paper, we show that Anderson acceleration with Chebyshev polynomial can achieve the optimal convergence rate $O(\sqrt{\kappa}\ln\frac{1}{\epsilon})$, which improves the previous result $O(\kappa\ln\frac{1}{\epsilon})$ provided by (Toth & Kelley, 2015) for quadratic functions. Moreover, we provide a convergence analysis for minimizing general nonlinear problems. Besides, if the hyperparameters (e.g., the Lipschitz smooth parameter $L$) are not available, we propose a \emph{guessing algorithm} for guessing them dynamically and also prove a similar convergence rate. Finally, the experimental results demonstrate that the proposed Anderson-Chebyshev acceleration method converges significantly faster than other algorithms, e.g., vanilla gradient descent (GD), Nesterov’s Accelerated GD. Also, these algorithms combined with the proposed guessing algorithm (guessing the hyperparameters dynamically) achieve much better performance.

In many classic clustering problems, we seek to sketch a massive data set of n points (a.k.a clients) in a metric space, by segmenting them into k categories or clusters, each cluster represented concisely by a single point in the metric space (a.k.a. the cluster’s center or its facility). The goal is to find such a sketch that minimizes some objective that depends on the distances between the clients and their respective facilities (the objective is a.k.a. the service cost). Two notable examples are the k-center/k-supplier problem where the objective is to minimize the maximum distance from any client to its facility, and the k-median problem where the objective is to minimize the sum over all clients of the distance from the client to its facility. In practical applications of clustering, the data set may evolve over time, reflecting an evolution of the underlying clustering model. Thus, in such applications, a good clustering must simultaneously represent the temporal data set well, but also not change too drastically between time steps. In this paper, we initiate the study of a dynamic version of clustering problems that aims to capture these considerations. In this version there are T time steps, and in each time step t ∈ {1,2,… ,T}, the set of clients needed to be clustered may change, and we can move the k facilities between time steps. The general goal is to minimize certain combinations of the service cost and the facility movement cost, or minimize one subject to some constraints on the other. More specifically, we study two concrete problems in this framework: the Dynamic Ordered k-Median and the Dynamic k-Supplier problem. Our technical contributions are as follows: - We consider the Dynamic Ordered k-Median problem, where the objective is to minimize the weighted sum of ordered distances over all time steps, plus the total cost of moving the facilities between time steps. We present one constant-factor approximation algorithm for T = 2 and another approximation algorithm for fixed T ≥ 3. - We consider the Dynamic k-Supplier problem, where the objective is to minimize the maximum distance from any client to its facility, subject to the constraint that between time steps the maximum distance moved by any facility is no more than a given threshold. When the number of time steps T is 2, we present a simple constant factor approximation algorithm and a bi-criteria constant factor approximation algorithm for the outlier version, where some of the clients can be discarded. We also show that it is NP-hard to approximate the problem with any factor for T ≥ 3.

Revenue prediction is an essential component in security analysis since the revenue of a company has a great impact on the performance of its stock. For investment, one of the most valuable pieces of information is the company’s unexpected revenue, which is the difference between the officially reported revenue and the consensus estimate for revenue predicted by analysts. Since it is the unexpected revenue that indicates something exceeding or under analysts’ expectation, it is an indispensable factor that influences the performance of a stock. Besides conventional trading data from stock market and companies’ financial reports, recent years have witnessed an extensive application of alternative data for gaining an information edge in stock investment.In this paper, we study the challenging problem of better predicting unexpected revenue of a company via machine learning with alternative data. To the best of our knowledge, this is the first work studying this problem in literature. However, it is nontrivial to quantitatively model the relations between the unexpected revenue and the information provided by alternative data with a machine learning approach. Thus we proposed an adaptive master-slave regularized model, called AMS for short, to effectively leverage alternative data for unexpected revenue prediction. AMS first trains a master model upon a company graph, which captures the relations among companies, using a graph neural network (GNN). Then for a target company, the master model generates an adaptive slave-model, which is specially optimized for this target company. Finally, we use this slave-model to predict the unexpected revenue of the target company. Besides its excellent prediction performance, another critical advantage of our AMS model lies in its superior interpretability, which is crucial for portfolio managers to understand the predicted results. With extensive experiments using two real-world alternative datasets, we have demonstrated the effectiveness of our model against a set of competitors.

Modern machine learning models (such as deep neural networks and boosting decision tree models) have become increasingly popular in financial market prediction, due to their superior capacity to extract complex non-linear patterns. However, since financial datasets have very low signal-to-noise ratio and are non-stationary, complex models are often very prone to overfitting and suffer from instability issues. Moreover, as various machine learning and data mining tools become more widely used in quantitative trading, many trading firms have been producing an increasing number of features (aka factors). Therefore, how to automatically select effective features becomes an imminent problem. To address these issues, we propose DoubleEnsemble, an ensemble framework leveraging learning trajectory based sample reweighting and shuffling based feature selection. Specifically, we identify the key samples based on the training dynamics on each sample and elicit key features based on the ablation impact of each feature via shuffling. Our model is applicable to a wide range of base models, capable of extracting complex patterns, while mitigating the overfitting and instability issues for financial market prediction. We conduct extensive experiments, including price prediction for cryptocurrencies and stock trading, using both DNN and gradient boosting decision tree as base models. Our experiment results demonstrate that DoubleEnsemble achieves a superior performance compared with several baseline methods.

Given a metric (V,d) and a root ∈ V, the classic k-TSP problem is to find a tour originating at the root of minimum length that visits at least k nodes in V. In this work, motivated by applications where the input to an optimization problem is uncertain, we study two stochastic versions of k-TSP. In Stoch-Reward k-TSP, originally defined by Ene-Nagarajan-Saket [Ene et al., 2018], each vertex v in the given metric (V,d) contains a stochastic reward R_v. The goal is to adaptively find a tour of minimum expected length that collects at least reward k; here "adaptively" means our next decision may depend on previous outcomes. Ene et al. give an O(log k)-approximation adaptive algorithm for this problem, and left open if there is an O(1)-approximation algorithm. We totally resolve their open question, and even give an O(1)-approximation non-adaptive algorithm for Stoch-Reward k-TSP. We also introduce and obtain similar results for the Stoch-Cost k-TSP problem. In this problem each vertex v has a stochastic cost C_v, and the goal is to visit and select at least k vertices to minimize the expected sum of tour length and cost of selected vertices. Besides being a natural stochastic generalization of k-TSP, this problem is also interesting because it generalizes the Price of Information framework [Singla, 2018] from deterministic probing costs to metric probing costs. Our techniques are based on two crucial ideas: "repetitions" and "critical scaling". In general, replacing a random variable with its expectation leads to very poor results. We show that for our problems, if we truncate the random variables at an ideal threshold, then their expected values form a good surrogate. Here, we rely on running several repetitions of our algorithm with the same threshold, and then argue concentration using Freedman’s and Jogdeo-Samuels' inequalities. Unfortunately, this ideal threshold depends on how far we are from achieving our target k, which a non-adaptive algorithm does not know. To overcome this barrier, we truncate the random variables at various different scales and identify a "critical" scale.

Speech synthesis (text to speech, TTS) and recognition (automatic speech recognition, ASR) are important speech tasks, and require a large amount of text and speech pairs for model training. However, there are more than 6,000 languages in the world and most languages are lack of speech training data, which poses significant challenges when building TTS and ASR systems for extremely low-resource languages. In this paper, we develop LRSpeech, a TTS and ASR system under the extremely low-resource setting, which can support rare languages with low data cost. LRSpeech consists of three key techniques: 1) pre-training on rich-resource languages and fine-tuning on low-resource languages; 2) dual transformation between TTS and ASR to iteratively boost the accuracy of each other; 3) knowledge distillation to customize the TTS model on a high-quality target-speaker voice and improve the ASR model on multiple voices. We conduct experiments on an experimental language (English) and a truly low-resource language (Lithuanian) to verify the effectiveness of LRSpeech. Experimental results show that LRSpeech 1) achieves high quality for TTS in terms of both intelligibility (more than $98%$ intelligibility rate) and naturalness (above 3.5 mean opinion score (MOS)) of the synthesized speech, which satisfy the requirements for industrial deployment, 2) achieves promising recognition accuracy for ASR, and 3) last but not least, uses extremely low-resource training data. We also conduct comprehensive analyses on LRSpeech with different amounts of data resources, and provide valuable insights and guidances for industrial deployment. We are currently deploying LRSpeech into a commercialized cloud speech service to support TTS on more rare languages.

Outlier detection is critical to a large number of applications from finance fraud detection to health care. Although numerous approaches have been proposed to automatically detect outliers, such outliers detected based on statistical rarity do not necessarily correspond to the true outliers to the interest of applications. In this work, we propose a human-in-the-loop outlier detection approach HOD that effectively leverages human intelligence to discover the true outliers. There are two main challenges in HOD. The first is to design human-friendly questions such that humans can easily understand the questions even if humans know nothing about the outlier detection techniques. The second is to minimize the number of questions. To address the first challenge, we design a clustering-based method to effectively discover a small number of objects that are unlikely to be outliers (aka, inliers) and yet effectively represent the typical characteristics of the given dataset. HOD then leverages this set of inliers (called context inliers) to help humans understand the context in which the outliers occur. This ensures humans are able to easily identify the true outliers from the outlier candidates produced by the machine-based outlier detection techniques. To address the second challenge, we propose a bipartite graph-based question selection strategy that is theoretically proven to be able to minimize the number of questions needed to cover all outlier candidates. Our experimental results on real data sets show that HOD significantly outperforms the state-of-the-art methods on both human efforts and the quality of the discovered outliers.

We study the problem of utilizing human intelligence to categorize a large number of objects. In this problem, given a category hierarchy and a set of objects, we can ask humans to check whether an object belongs to a category, and our goal is to find the most cost-effective strategy to locate the appropriate category in the hierarchy for each object, such that the cost (i.e., the number of questions to ask humans) is minimized. There are many important applications of this problem, including image classification and product categorization. We develop an online framework, in which category distribution is gradually learned and thus an effective order of questions are adaptively determined. We prove that even if the true category distribution is known in advance, the problem is computationally intractable. We develop an approximation algorithm, and prove that it achieves an approximation factor of 2. We also show that there is a fully polynomial time approximation scheme for the problem. Furthermore, we propose an online strategy which achieves nearly the same performance guarantee as the offline optimal strategy, even if there is no knowledge about category distribution beforehand. Experiments on a real crowdsourcing platform demonstrate the effectiveness of our method.

Gradient Boosted Decision Trees (GBDT) is a very successful ensemble learning algorithm widely used across a variety of applications. Recently, several variants of GBDT training algorithms and implementations have been designed and heavily optimized in some very popular open sourced toolkits including XGBoost, LightGBM and CatBoost. In this paper, we show that both the accuracy and efficiency of GBDT can be further enhanced by using more complex base learners. Specifically, we extend gradient boosting to use piecewise linear regression trees (PL Trees), instead of piecewise constant regression trees, as base learners. We show that PL Trees can accelerate convergence of GBDT and improve the accuracy. We also propose some optimization tricks to substantially reduce the training time of PL Trees, with little sacrifice of accuracy. Moreover, we propose several implementation techniques to speedup our algorithm on modern computer architectures with powerful Single Instruction Multiple Data (SIMD) parallelism. The experimental results show that GBDT with PL Trees can provide very competitive testing accuracy with comparable or less training time.

We study the problem of large-scale network embedding, which aims to learn latent representations for network mining applications. Previous research shows that 1) popular network embedding benchmarks, such as DeepWalk, are in essence implicitly factorizing a matrix with a closed form, and 2) the explicit factorization of such matrix generates more powerful embeddings than existing methods. However, directly constructing and factorizing this matrix-which is dense-is prohibitively expensive in terms of both time and space, making it not scalable for large networks.

Estimating the travel time of any path (denoted by a sequence of connected road segments) in a city is of great importance to traffic monitoring, route planning, ridesharing, taxi/Uber dispatching, etc. However, it is a very challenging problem, affected by diverse complex factors, including spatial correlations, temporal dependencies, external conditions (e.g. weather, traffic lights). Prior work usually focuses on estimating the travel times of individual road segments or sub-paths and then summing up these times, which leads to an inaccurate estimation because such approaches do not consider road intersections/traffic lights, and local errors may accumulate. To address these issues, we propose an end-to-end Deep learning framework for Travel Time Estimation called DeepTTE that estimates the travel time of the whole path directly. More specifically, we present a geo-convolution operation by integrating the geographic information into the classical convolution, capable of capturing spatial correlations. By stacking recurrent unit on the geo-convoluton layer, our DeepTTE can capture the temporal dependencies simultaneously. A multi-task learning component is given on the top of DeepTTE, that estimates the travel time of both the entire path and each local path simultaneously during the training phase. The extensive experiments on two large-scale datasets shows our DeepTTE significantly outperforms the state-of-the-art methods.

It is a long standing open problem whether Yao-Yao graphs YY_{k} are all spanners [Li et al. 2002]. Bauer and Damian [Bauer and Damian, 2012] showed that all YY_{6k} for k >= 6 are spanners. Li and Zhan [Li and Zhan, 2016] generalized their result and proved that all even Yao-Yao graphs YY_{2k} are spanners (for k >= 42). However, their technique cannot be extended to odd Yao-Yao graphs, and whether they are spanners are still elusive. In this paper, we show that, surprisingly, for any integer k >= 1, there exist odd Yao-Yao graph YY_{2k+1} instances, which are not spanners.

Suffix array is a fundamental data structure for many applications that involve string searching and data compression. We obtain the first linear time inplace suffix array construction algorithm which is optimal both in time and space for read-only integer alphabets. Our algorithm settles the open problem posed by Franceschini and Muthukrishnan [1]. The open problem asked to design in-place algorithms in o(n log n) time and ultimately, in O(n) time for integer alphabets with |Σ| ≤ n. Our result is in fact slightly stronger since we allow |Σ| = O(n). Besides, we extend it to obtain an optimal O(n log n) time in-place suffix sorting algorithm for read-only general alphabets (i.e., only comparisons are allowed).

We study the problem of constructing ε-coresets for the (k, z)-clustering problem in a doubling metric M(X, d). An ε-coreset is a weighted subset S ⊆ X with weight function w : S → ℝ≥0, such that for any k-subset C ∈ [X]k, it holds that Σx∈Sw(x) · dz(x, C) ∈ (1 ± ε) · Σx∈Xdz(x, C). We present an efficient algorithm that constructs an ε-coreset for the (k, z)-clustering problem in M(X, d), where the size of the coreset only depends on the parameters k, z, ε and the doubling dimension ddim(M). To the best of our knowledge, this is the first efficient c-coreset construction of size independent of |X| for general clustering problems in doubling metrics. To this end, we establish the first relation between the doubling dimension of M(X, d) and the shattering dimension (or VC-dimension) of the range space induced by the distance d. Such a relation is not known before, since one can easily construct instances in which neither one can be bounded by (some function of) the other. Surprisingly, we show that if we allow a small (1 ± ε)-distortion of the distance function d (the distorted distance is called the smoothed distance function), the shattering dimension can be upper bounded by O(ε-O(ddim(M))). For the purpose of coreset construction, the above bound does not suffice as it only works for unweighted spaces. Therefore, we introduce the notion of τ-error probabilistic shattering dimension, and prove a (drastically better) upper bound of O(ddim(M)·log(1/ε)+log log 1/τ) for the probabilistic shattering dimension for weighted doubling metrics. As it turns out, an upper bound for the probabilistic shattering dimension is enough for constructing a small coreset. We believe the new relation between doubling and shattering dimensions is of independent interest and may find other applications. Furthermore, we study robust coresets for (k, z)-clustering with outliers in a doubling metric. We show an improved connection between α-approximation and robust coresets. This also leads to improvement upon the previous best known bound of the size of robust coreset for Euclidean space [Feldman and Langberg, STOC 11]. The new bound entails a few new results in clustering and property testing. As another application, we show constant-sized (ε, k, z)centroid sets in doubling metrics can be constructed by extending our coreset construction. Prior to our result, constantsized centroid sets for general clustering problems were only known for Euclidean spaces. We can apply our centroid set to accelerate the local search algorithm (studied in [Friggstad et al., FOCS 2016]) for the (k, z)-clustering problem in doubling metrics.

Time series are widely used as signals in many classification/regression tasks. It is ubiquitous that time series contains many missing values. Given multiple correlated time series data, how to fill in missing values and to predict their class labels? Existing imputation methods often impose strong assumptions of the underlying data generating process, such as linear dynamics in the state space. In this paper, we propose BRITS, a novel method based on recurrent neural networks for missing value imputation in time series data. Our proposed method directly learns the missing values in a bidirectional recurrent dynamical system, without any specific assumption. The imputed values are treated as variables of RNN graph and can be effectively updated during the backpropagation. BRITS has three advantages: (a) it can handle multiple correlated missing values in time series; (b) it generalizes to time series with nonlinear dynamics underlying; (c) it provides a data-driven imputation procedure and applies to general settings with missing data. We evaluate our model on three real-world datasets, including an air quality dataset, a health-care data, and a localization data for human activity. Experiments show that our model outperforms the state-of-the-art methods in both imputation and classification/regression accuracies.

We analyze stochastic gradient algorithms for optimizing nonconvex, nonsmooth finite-sum problems. In particular, the objective function is given by the summation of a differentiable (possibly nonconvex) component, together with a possibly non-differentiable but convex component. We propose a proximal stochastic gradient algorithm based on variance reduction, called ProxSVRG+. Our main contribution lies in the analysis of ProxSVRG+. It recovers several existing convergence results and improves/generalizes them (in terms of the number of stochastic gradient oracle calls and proximal oracle calls). In particular, ProxSVRG+ generalizes the best results given by the SCSG algorithm, recently proposed by [Lei et al., NIPS'17] for the smooth nonconvex case. ProxSVRG+ is also more straightforward than SCSG and yields simpler analysis. Moreover, ProxSVRG+ outperforms the deterministic proximal gradient descent (ProxGD) for a wide range of minibatch sizes, which partially solves an open problem proposed in [Reddi et al., NIPS'16]. Also, ProxSVRG+ uses much less proximal oracle calls than ProxSVRG [Reddi et al., NIPS'16]. Moreover, for nonconvex functions satisfied Polyak-\L{}ojasiewicz condition, we prove that ProxSVRG+ achieves a global linear convergence rate without restart unlike ProxSVRG. Thus, it can \emph{automatically} switch to the faster linear convergence in some regions as long as the objective function satisfies the PL condition locally in these regions. Finally, we conduct several experiments and the experimental results are consistent with the theoretical results.

Extracting interesting tuples from a large database is an important problem in multi-criteria decision making. Two representative queries were proposed in the literature: top- k queries and skyline queries. A top- k query requires users to specify their utility functions beforehand and then returns k tuples to the users. A skyline query does not require any utility function from users but it puts no control on the number of tuples returned to users. Recently, a k-regret query was proposed and received attention from the community because it does not require any utility function from users and the output size is controllable, and thus it avoids those deficiencies of top- k queries and skyline queries. Specifically, it returns k tuples that minimize a criterion called the maximum regret ratio .

Since the invention of word2vec, the skip-gram model has significantly advanced the research of network embedding, such as the recent emergence of the DeepWalk, LINE, PTE, and node2vec approaches. In this work, we show that all of the aforementioned models with negative sampling can be unified into the matrix factorization framework with closed forms. Our analysis and proofs reveal that: (1) DeepWalk empirically produces a low-rank transformation of a network's normalized Laplacian matrix; (2) LINE, in theory, is a special case of DeepWalk when the size of vertices' context is set to one; (3) As an extension of LINE, PTE can be viewed as the joint factorization of multiple networks» Laplacians; (4) node2vec is factorizing a matrix related to the stationary distribution and transition probability tensor of a 2nd-order random walk. We further provide the theoretical connections between skip-gram based network embedding algorithms and the theory of graph Laplacian. Finally, we present the NetMF method as well as its approximation algorithm for computing network embedding. Our method offers significant improvements over DeepWalk and LINE for conventional network mining tasks. This work lays the theoretical foundation for skip-gram based network embedding methods, leading to a better understanding of latent network representation learning.

Crowd-powered database systems can leverage the crowd's ability to address machine-hard problems, e.g., data integration. Existing crowdsourcing systems adopt the traditional tree model to select a good query plan. However, the tree model can optimize the I/O cost but cannot optimize the monetary cost, latency and quality, which are three important optimization goals in crowdsourcing. To address this limitation, we demonstrate CDB, a crowd-powered database system. CDB proposes a new graph-based model that adopts a fine-grained tuple-level optimization model which significantly outperforms existing coarse-grained tree-based optimization models. Moreover, CDB provides a unified framework to simultaneously optimize the monetary cost, quality and latency. We have deployed CDB on well-known crowd-sourcing platforms and users can easily use our system to deploy their applications. We will demonstrate how to use CDB to address real-world applications, including web table integration and entity collection.

In the Best-k-Arm problem, we are given n stochastic bandit arms, each associated with an unknown reward distribution. We are required to identify the k arms with the largest means by taking as few samples as possible. In this paper, we make progress towards a complete characterization of the instance-wise sample complexity bounds for the Best-k-Arm problem. On the lower bound side, we obtain a novel complexity term to measure the sample complexity that every Best-k-Arm instance requires. This is derived by an interesting and nontrivial reduction from the Best-1-Arm problem. We also provide an elimination-based algorithm that matches the instance-wise lower bound within doubly-logarithmic factors. The sample complexity of our algorithm strictly dominates the state-of-the-art for Best-k-Arm (module constant factors).

We study the combinatorial pure exploration problem \textscBest-Set in a stochastic multi-armed bandit game. In an \textscBest-Set instance, we are given $n$ stochastic arms with unknown reward distributions, as well as a family $\mathcal{F}$ of feasible subsets over the arms. Let the weight of an arm be the mean of its reward distribution. Our goal is to identify the feasible subset in $\mathcal{F}$ with the maximum total weight, using as few samples as possible. The problem generalizes the classical best arm identification problem and the top-$k$ arm identification problem, both of which have attracted significant attention in recent years. We provide a novel \textitinstance-wise lower bound for the sample complexity of the problem, as well as a nontrivial sampling algorithm, matching the lower bound up to a factor of $\ln|\mathcal{F}|$. For an important class of combinatorial families (including spanning trees, matchings, and path constraints), we also provide polynomial time implementation of the sampling algorithm, using the equivalence of separation and optimization for convex program, and the notion of approximate Pareto curves in multi-objective optimization (note that $|\mathcal{F}|$ can be exponential in $n$). We also show that the $\ln|\mathcal{F}|$ factor is inevitable in general, through a nontrivial lower bound construction utilizing a combinatorial structure resembling the Nisan-Wigderson design. Our results significantly improve several previous results for several important combinatorial constraints, and provide a tighter understanding of the general \textscBest-Set problem. We further introduce an even more general problem, formulated in geometric terms. We are given $n$ Gaussian arms with unknown means and unit variance. Consider the $n$-dimensional Euclidean space $\mathbb{R}^n$, and a collection $\mathcal{O}$ of disjoint subsets. Our goal is to determine the subset in $\mathcal{O}$ that contains the mean profile (which is the $n$-dimensional vector of the means), using as few samples as possible. The problem generalizes most pure exploration bandit problems studied in the literature. We provide the first nearly optimal sample complexity upper and lower bounds for the problem.

In the classical best arm identification (Best-$1$-Arm) problem, we are given $n$ stochastic bandit arms, each associated with a reward distribution with an unknown mean. Upon each play of an arm, we can get a reward sampled i.i.d. from its reward distribution. We would like to identify the arm with the largest mean with probability at least $1-δ$, using as few samples as possible. The problem has a long history and understanding its sample complexity has attracted significant attention since the last decade. However, the optimal sample complexity of the problem is still unknown. Recently, Chen and Li (2016) made an interesting conjecture, called gap-entropy conjecture, concerning the instance optimal sample complexity of Best-$1$-Arm. Given a Best-$1$-Arm instance $I$ (i.e., a set of arms), let $\mu_[i]$ denote the $i$th largest mean and $\Delta_[i]=\mu_[1]-\mu_[i]$ denote the corresponding gap. $H(I)=\sum_i=2^n\Delta_[i]^-2$ denotes the complexity of the instance. The gap-entropy conjecture states that for any instance $I$, $Ω\left(H(I)⋅\left(\lnδ^-1 + \mathsf{Ent}(I)\right)\right)$ is an instance lower bound, where $\mathsf{Ent}(I)$ is an entropy-like term determined by the gaps, and there is a $δ$-correct algorithm for Best-$1$-Arm with sample complexity $O\left(H(I)⋅\left(\lnδ^-1 + \mathsf{Ent}(I)\right)+\Delta_[2]^-2\ln\ln\Delta_[2]^-1\right)$. We note that $Θ\left(\Delta_[2]^-2\ln\ln\Delta_[2]^-1\right)$ is necessary and sufficient to solve the two-arm instance with the best and second best arms. If the conjecture is true, we would have a complete understanding of the instance-wise sample complexity of Best-$1$-Arm (up to constant factors). In this paper, we make significant progress towards a complete resolution of the gap-entropy conjecture. For the upper bound, we provide a highly nontrivial algorithm which requires \[O\left(H(I)⋅\left(\lnδ^-1 + \mathsf{Ent}(I)\right)+\Delta_[2]^-2\ln\ln\Delta_[2]^-1\mathrmpolylog(n,δ^-1)\right)\]samples in expectation for any instance $I$. For the lower bound, we show that for any Gaussian Best-$1$-Arm instance with gaps of the form $2^-k$, any $δ$-correct monotone algorithm requires at least \[Ω\left(H(I)⋅\left(\lnδ^-1 + \mathsf{Ent}(I)\right)\right)\]samples in expectation. Here, a monotone algorithm is one which uses no more samples (in expectation) on $I’$ than on $I$, if $I’$ is a sub-instance of $I$ obtained by removing some sub-optimal arms.

We study the data cleaning problem of detecting and repairing wrong relational data, as well as marking correct data, using well curated knowledge bases (KBs). We propose detective rules (DRs), a new type of data cleaning rules that can make actionable decisions on relational data, by building connections between a relation and a KB. The main invention is that, a DR simultaneously models two opposite semantics of a relation using types and relationships in a KB: the positive semantics that explains how attribute values are linked to each other in correct tuples, and the negative semantics that indicates how wrong attribute values are connected to other correct attribute values within the same tuples. Naturally, a DR can mark correct values in a tuple if it matches the positive semantics. Meanwhile, a DR can detect/repair an error if it matches the negative semantics. We study fundamental problems associated with DRs, e.g., rule generation and rule consistency. We present efficient algorithms to apply DRs to clean a relation, based on rule order selection and inverted indexes. Extensive experiments, using both real-world and synthetic datasets, verify the effectiveness and efficiency of applying DRs in practice.

The online car-hailing service has gained great popularity all over the world. As more passengers and more drivers use the service, it becomes increasingly more important for the the car-hailing service providers to effectively schedule the drivers to minimize the waiting time of passengers and maximize the driver utilization, thus to improve the overall user experience. In this paper, we study the problem of predicting the real-time car-hailing supply-demand, which is one of the most important component of an effective scheduling system. Our objective is to predict the gap between the car-hailing supply and demand in a certain area in the next few minutes. Based on the prediction, we can balance the supply-demands by scheduling the drivers in advance. We present an end-to-end framework called Deep Supply-Demand (DeepSD) using a novel deep neural network structure. Our approach can automatically discover complicated supply-demand patterns from the car-hailing service data while only requires a minimal amount hand-crafted features. Moreover, our framework is highly flexible and extendable. Based on our framework, it is very easy to utilize multiple data sources (e.g., car-hailing orders, weather and traffic data) to achieve a high accuracy. We conduct extensive experimental evaluations, which show that our framework provides more accurate prediction results than the existing methods.

We study the k-regret minimizing query (k-RMS), which is a useful operator for supporting multi-criteria decision-making. Given two integers k and r, a k-RMS returns r tuples from the database which minimize the k-regret ratio, defined as one minus the worst ratio between the k-th maximum utility score among all tuples in the database and the maximum utility score of the r tuples returned. A solution set contains only r tuples, enjoying the benefits of both top-k queries and skyline queries. Proposed in 2012, the query has been studied extensively in recent years. In this paper, we advance the theory and the practice of k-RMS in the following aspects. First, we develop efficient algorithms for k-RMS (and its decision version) when the dimensionality is 2. The running time of our algorithms outperforms those of previous ones. Second, we show that k-RMS is NP-hard even when the dimensionality is 3. This provides a complete characterization of the complexity of k-RMS, and answers an open question in previous studies. In addition, we present approximation algorithms for the problem when the dimensionality is 3 or larger.

Training deep neural networks is a highly nontrivial task, involving carefully selecting appropriate training algorithms, scheduling step sizes and tuning other hyperparameters. Trying different combinations can be quite labor-intensive and time consuming. Recently, researchers have tried to use deep learning algorithms to exploit the landscape of the loss function of the training problem of interest, and learn how to optimize over it in an automatic way. In this paper, we propose a new learning-to-learn model and some useful and practical tricks. Our optimizer outperforms generic, hand-crafted optimization algorithms and state-of-the-art learning-to-learn optimizers by DeepMind in many tasks. We demonstrate the effectiveness of our algorithms on a number of tasks, including deep MLPs, CNNs, and simple LSTMs.

Crowdsourcing database systems have been proposed to leverage crowd-powered operations to encapsulate the complexities of interacting with the crowd. Existing systems suffer from two major limitations. Firstly, in order to optimize a query, they often adopt the traditional tree model to select an optimized table-level join order. However, the tree model provides a coarse-grained optimization, which generates the same order for different joined tuples and limits the optimization potential that different joined tuples can be optimized by different orders. Secondly, they mainly focus on optimizing the monetary cost. In fact, there are three optimization goals (i.e., smaller monetary cost, lower latency, and higher quality) in crowdsourcing, and it calls for a system to enable multi-goal optimization.

Solving geometric optimization problems over uncertain data has become increasingly important in many applications and has attracted a lot of attentions in recent years. In this paper, we study two important geometric optimization problems, the k-center problem and the j-flat-center problem, over stochastic/uncertain data points in Euclidean spaces. For the stochastic k-center problem, we would like to find k points in a fixed dimensional Euclidean space, such that the expected value of the k-center objective is minimized. For the stochastic j-flat-center problem, we seek a j-flat (i.e., a j-dimensional affine subspace) such that the expected value of the maximum distance from any point to the j-flat is minimized. We consider both problems under two popular stochastic geometric models, the existential uncertainty model, where the existence of each point may be uncertain, and the locational uncertainty model, where the location of each point may be uncertain. We provide the first PTAS (Polynomial Time Approximation Scheme) for both problems under the two models. Our results generalize the previous results for stochastic minimum enclosing ball and stochastic enclosing cylinder.

We study the pure exploration problem subject to a matroid constraint (Best-Basis) in a stochastic multi-armed bandit game. In a Best-Basis instance, we are given n stochastic arms with unknown reward distributions, as well as a matroid \mathcalM over the arms. Let the weight of an arm be the mean of its reward distribution. Our goal is to identify a basis of \mathcalM with the maximum total weight, using as few samples as possible. The problem is a significant generalization of the best arm identification problem and the top-k arm identification problem, which have attracted significant attentions in recent years. We study both the exact and PAC versions of Best-Basis, and provide algorithms with nearly-optimal sample complexities for these versions. Our results generalize and/or improve on several previous results for the top-k arm identification problem and the combinatorial pure exploration problem when the combinatorial constraint is a matroid.

The best arm identification problem (BEST-1-ARM) is the most basic pure exploration problem in stochastic multi-armed bandits. The problem has a long history and attracted significant attention for the last decade. However, we do not yet have a complete understanding of the optimal sample complexity of the problem: The state-of-the-art algorithms achieve a sample complexity of O(\sum_i=2^n \Delta_i^-2(\lnδ^-1 + \ln\ln\Delta_i^-1)) (\Delta_i is the difference between the largest mean and the i^th mean), while the best known lower bound is Ω(\sum_i=2^n \Delta_i^-2\lnδ^-1) for general instances and Ω(∆^-2 \ln\ln ∆^-1) for the two-arm instances. We propose to study the instance-wise optimality for the BEST-1-ARM problem. Previous work has proved that it is impossible to have an instance optimal algorithm for the 2-arm problem. However, we conjecture that modulo the additive term Ω(\Delta_2^-2 \ln\ln \Delta_2^-1) (which is an upper bound and worst case lower bound for the 2-arm problem), there is an instance optimal algorithm for BEST-1-ARM. Moreover, we introduce a new quantity, called the gap entropy for a best-arm problem instance, and conjecture that it is the instance-wise lower bound. Hence, resolving this conjecture would provide a final answer to the old and basic problem.

With the dramatic growth in the number of application domains that generate probabilistic, noisy and uncertain data, there has been an increasing interest in designing algorithms for geometric or combinatorial optimization problems over such data. In this paper, we initiate the study of constructing epsilon-kernel coresets for uncertain points. We consider uncertainty in the existential model where each point's location is fixed but only occurs with a certain probability, and the locational model where each point has a probability distribution describing its location. An epsilon-kernel coreset approximates the width of a point set in any direction. We consider approximating the expected width (an epsilon-EXP-KERNEL), as well as the probability distribution on the width (an (epsilon, tau)-QUANT-KERNEL) for any direction. We show that there exists a set of O(epsilon^{-(d-1)/2}) deterministic points which approximate the expected width under the existential and locational models, and we provide efficient algorithms for constructing such coresets. We show, however, it is not always possible to find a subset of the original uncertain points which provides such an approximation. However, if the existential probability of each point is lower bounded by a constant, an epsilon-EXP-KERNEL is still possible. We also provide efficient algorithms for construct an (epsilon, tau)-QUANT-KERNEL coreset in nearly linear time. Our techniques utilize or connect to several important notions in probability and geometry, such as Kolmogorov distances, VC uniform convergence and Tukey depth, and may be useful in other geometric optimization problem in stochastic settings. Finally, combining with known techniques, we show a few applications to approximating the extent of uncertain functions, maintaining extent measures for stochastic moving points and some shape fitting problems under uncertainty.

It is an open problem whether Yao-Yao graphs YY_{k} (also known as sparse-Yao graphs) are all spanners when the integer parameter k is large enough. In this paper we show that, for any integer k >= 42, the Yao-Yao graph YY_{2k} is a t_k-spanner, with stretch factor t_k = 6.03+O(k^{-1}) when k tends to infinity. Our result generalizes the best known result which asserts that all YY_{6k} are spanners for k >= 6 [Bauer and Damian, SODA'13]. Our proof is also somewhat simpler.

Choosing a good location when opening a new store is crucial for the future success of a business. Traditional methods include offline manual survey, analytic models based on census data, which are either unable to adapt to the dynamic market or very time consuming. The rapid increase of the availability of big data from various types of mobile devices, such as online query data and offline positioning data, provides us with the possibility to develop automatic and accurate data- driven prediction models for business store site selection. In this paper, we propose a Demand Driven Store Site Selection (DD3S) framework for business store site selection by mining search query data from Baidu Maps. DD3S first detects the spatial-temporal distributions of customer demands on different business services via query data from Baidu Maps, the largest online map search engine in China, and detects the gaps between demand and supply. Then we determine candidate locations via clustering such gaps. In the final stage, we solve the location optimization problem by predicting and ranking the number of customers. We not only deploy supervised regression models to predict the number of customers, but also use learning-to-rank model to directly rank the locations. We evaluate our framework on various types of businesses in real-world cases, and the experiment results demonstrate the effectiveness of our methods. DD3S as the core function for store site selection has already been implemented as a core component of our business analytics platform and could be potentially used by chain store merchants on Baidu Nuomi.

With the wide use of mobile devices, predicting the destination of moving vehicles has become an increasingly important problem for location based recommendation systems and destination-based advertising. Most existing approaches are based on various Markov chain models, in which the historical trajectories are used to train the model and the top-k most probable destinations are returned. We identify certain limitations of the previous approaches. Instead, we propose a new data-driven framework, called DestPre, which is not based on a probabilistic model, but directly operates on the trajectories and makes the prediction. We make use of only historic trajectories, without individual identity information. Our design of DestPre, although simple, is a result of several useful observations from the real trajectory data. DestPre involves an index based on Bucket PR Quadtree and Minwise hashing, for efficiently retrieving similar trajectories, and a clustering on destinations for predictions. By incorporating some additional ideas, we show that the prediction accuracy can be further improved. We have conducted extensive experiments on real Beijing Taxi dataset. The experimental results demonstrate the effectiveness of DestPre.

With the ubiquity of location based services and applications, large volume of mobility data has been generated routinely, usually from heterogeneous data sources, such as different GPS-embedded devices, mobile apps or location based service providers. In this paper, we investigate efficient ways of identifying users across such heterogeneous data sources. We present a MapReduce-based framework called Automatic User Identification (AUI) which is easy to deploy and can scale to very large data set. Our framework is based on a novel similarity measure called the signal based similarity (SIG) which measures the similarity of users' trajectories gathered from different data sources, typically with very different sampling rates and noise patterns. We conduct extensive experimental evaluations, which show that our framework outperforms the existing methods significantly. Our study on one hand provides an effective approach for the mobility data integration problem on large scale data sets, i.e., combining the mobility data sets from different sources in order to enhance the data quality. On the other hand, our study provides an in-depth investigation for the widely studied human mobility uniqueness problem under heterogeneous data sources.

Distributed clustering has attracted significant attention in recent years. In this paper, we study the k-means problem in the distributed dimension setting, where the dimensions of the data are partitioned across multiple machines. We provide new approximation algorithms, which incur low communication costs and achieve constant approximation ratios. The communication complexity of our algorithms significantly improve on existing algorithms. We also provide the first communication lower bound, which nearly matches our upper bound in a certain range of parameter setting. Our experimental results show that our algorithms outperform existing algorithms on real data-sets in the distributed dimension setting.

In this paper, we study the stochastic combinatorial multi-armed bandit (CMAB) framework that allows a general nonlinear reward function, whose expected value may not depend only on the means of the input random variables but possibly on the entire distributions of these variables. Our framework enables a much larger class of reward functions such as the $\max()$ function and nonlinear utility functions. Existing techniques relying on accurate estimations of the means of random variables, such as the upper confidence bound (UCB) technique, do not work directly on these functions. We propose a new algorithm called stochastically dominant confidence bound (SDCB), which estimates the distributions of underlying random variables and their stochastically dominant confidence bounds. We prove that SDCB can achieve $O(\log T)$ distribution-dependent regret and $\tilde{O}(\sqrt{T})$ distribution-independent regret, where $T$ is the time horizon. We apply our results to the $K$-MAX problem and expected utility maximization problems. In particular, for $K$-MAX, we provide the first polynomial-time approximation scheme (PTAS) for its offline problem, and give the first $\tilde{O}(\sqrt T)$ bound on the $(1-\epsilon)$-approximation regret of its online problem, for any $\epsilon>0$.

Crowdsourced entity resolution has recently attracted significant attentions because it can harness the wisdom of crowd to improve the quality of entity resolution. However existing techniques either cannot achieve high quality or incur huge monetary costs. To address these problems, we propose a cost-effective crowdsourced entity resolution framework, which significantly reduces the monetary cost while keeping high quality. We first define a partial order on the pairs of records. Then we select a pair as a question and ask the crowd to check whether the records in the pair refer to the same entity. After getting the answer of this pair, we infer the answers of other pairs based on the partial order. Next we iteratively select pairs without answers to ask until we get the answers of all pairs. We devise effective algorithms to judiciously select the pairs to ask in order to minimize the number of asked pairs. To further reduce the cost, we propose a grouping technique to group the pairs and we only ask one pair instead of all pairs in each group. We develop error-tolerant techniques to tolerate the errors introduced by the partial order and the crowd. Experimental results show that our method reduces the cost to 1.25% of existing approaches (or existing approaches take 80* monetary cost of our method) while not sacrificing the quality.

In this article, we consider the fault-tolerant k -median problem and give the first constant factor approximation algorithm for it. In the fault-tolerant generalization of the classical k -median problem, each client j needs to be assigned to at least r j ⩾ 1 distinct open facilities. The service cost of j is the sum of its distances to the r j facilities, and the k -median constraint restricts the number of open facilities to at most k . Previously, a constant factor was known only for the special case when all r j s are the same, and alogarithmic approximation ratio was known for the general case. In addition, we present the first polynomial time algorithm for the fault-tolerant k -median problem on a path or an HST by showing that the corresponding LP always has an integral optimal solution. We also consider the fault-tolerant facility location problem, in which the service cost of j can be a weighted sum of its distance to the r j facilities. We give a simple constant factor approximation algorithm, generalizing several previous results that work only for nonincreasing weight vectors.

This paper discusses how to efficiently choose from $n$ unknowndistributions the $k$ ones whose means are the greatest by a certainmetric, up to a small relative error. We study the topic under twostandard settings---multi-armed bandits and hidden bipartitegraphs---which differ in the nature of the input distributions. In theformer setting, each distribution can be sampled (in the i.i.d.manner) an arbitrary number of times, whereas in the latter, eachdistribution is defined on a population of a finite size $m$ (andhence, is fully revealed after $m$ samples). For both settings, weprove lower bounds on the total number of samples needed, and proposeoptimal algorithms whose sample complexities match those lower bounds.

The greedy algorithm is extensively studied in the field of combinatorial optimization for decades. In this paper, we address the online learning problem when the input to the greedy algorithm is stochastic with unknown parameters that have to be learned over time. We first propose the greedy regret and $\epsilon$-quasi greedy regret as learning metrics comparing with the performance of offline greedy algorithm. We then propose two online greedy learning algorithms with semi-bandit feedbacks, which use multi-armed bandit and pure exploration bandit policies at each level of greedy learning, one for each of the regret metrics respectively. Both algorithms achieve $O(\log T)$ problem-dependent regret bound ($T$ being the time horizon) for a general class of combinatorial structures and reward functions that allow greedy solutions. We further show that the bound is tight in $T$ and other problem instance parameters.

In this paper we study similarity join and search on multi- attribute data. Traditional methods on single-attribute data have pruning power only on single attributes and cannot efficiently support multi-attribute data. To address this problem, we propose a prefix tree index which has holis- tic pruning ability on multiple attributes. We propose a cost model to quantify the prefix tree which can guide the prefix tree construction. Based on the prefix tree, we devise a filter-verification framework to support similarity search and join on multi-attribute data. The filter step prunes a large number of dissimilar results and identifies some candi- dates using the prefix tree and the verification step verifies the candidates to generate the final answer. For similar- ity join, we prove that constructing an optimal prefix tree is NP-complete and develop a greedy algorithm to achieve high performance. For similarity search, since one prefix tree cannot support all possible search queries, we extend the cost model to support similarity search and devise a budget-based algorithm to construct multiple high-quality prefix trees. We also devise a hybrid verification algorithm to improve the verification step. Experimental results show our method significantly outperforms baseline approaches.

We study the problem of learning from unlabeled samples very general statistical mixture models on large finite sets. Specifically, the model to be learned, mix, is a probability distribution over probability distributions p, where each such p is a probability distribution over [n] = {1,2,...,n}. When we sample from mix, we do not observe p directly, but only indirectly and in very noisy fashion, by sampling from [n] repeatedly, independently K times from the distribution p. The problem is to infer mix to high accuracy in transportation (earthmover) distance.

In this paper, we propose an energy efficient device discovery protocol, eDiscovery, as the first step to bootstrapping opportunistic communications for smartphones, the most popular mobile devices. We chose Bluetooth over WiFi as the underlying wireless technology of device discovery, based on our measurement study of their operational power at different states on smartphones. eDiscovery adaptively changes the duration and interval of Bluetooth inquiry in dynamic environments, by leveraging history information of discovered peers. We implement a prototype of eDiscovery on Nokia N900 smartphones and evaluate its performance in three different environments. To the best of our knowledge, we are the first to conduct extensive performance evaluation of Bluetooth device discovery in the wild. Our experimental results demonstrate that compared with a scheme with constant inquiry duration and interval, eDiscovery can save around 44 percent energy at the expense of discovering only about 21 percent less peers. The results also show that eDiscovery performs better than other existing schemes, by discovering more peers and consuming less energy. We also verify the experimental results through extensive simulation studies in the ns-2 simulator.

We study the problem of selecting K arms with the highest expected rewards in a stochastic N-armed bandit game. Instead of using existing evaluation metrics (e.g., misidentification probability or the metric in EXPLORE-K), we propose to use the aggregate regret, which is defined as the gap between the average reward of the optimal solution and that of our solution. Besides being a natural metric by itself, we argue that in many applications, such as our motivating example from crowdsourcing, the aggregate regret bound is more suitable. We propose a new PAC algorithm, which, with probability at least 1-δ, identifies a set of K arms with regret at most ε. We provide the sample complexity bound of our algorithm. To complement, we establish the lower bound and show that the sample complexity of our algorithm matches the lower bound. Finally, we report experimental results on both synthetic and real data sets, which demonstrates the superior performance of the proposed algorithm.

We consider the multi-shop ski rental problem. This problem generalizes the classic ski rental problem to a multi-shop setting, in which each shop has different prices for renting and purchasing a pair of skis, and a consumer has to make decisions on when and where to buy. We are interested in the optimal online (competitive-ratio minimizing) mixed strategy from the consumer's perspective. For our problem in its basic form, we obtain exciting closed-form solutions and a linear time algorithm for computing them. We further demonstrate the generality of our approach by investigating three extensions of our basic problem, namely ones that consider costs incurred by entering a shop or switching to another shop. Our solutions to these problems suggest that the consumer must assign positive probability in exactly one shop at any buying time. Our results apply to many real-world applications, ranging from cost management in IaaS cloud to scheduling in distributed computing.

In this paper, we consider the fault-tolerant k-median problem and give the first constant factor approximation algorithm for it. In the fault-tolerant generalization of classical k-median problem, each client j needs to be assigned to at least rj ≥ 1 distinct open facilities. The service cost of j is the sum of its distances to the rj facilities, and the k-median constraint restricts the number of open facilities to at most k. Previously, a constant factor was known only for the special case when all rjs are the same, and a logarithmic approximation ratio was known for the general case. In addition, we present the first polynomial time algorithm for the fault-tolerant k-median problem on a path or a HST by showing that the corresponding LP always has an integral optimal solution. We also consider the fault-tolerant facility location problem, where the service cost of j can be a weighted sum of its distance to the rj facilities. We give a simple constant factor approximation algorithm, generalizing several previous results which only work for nonincreasing weight vectors.

We address the problem of approximate nearest neighbor (ANN) search for visual descriptor indexing. Most spatial partition trees, such as KD trees, VP trees, and so on, follow the hierarchical binary space partitioning framework. The key effort is to design different partition functions (hyperplane or hypersphere) to divide the points so that 1) the data points can be well grouped to support effective NN candidate location and 2) the partition functions can be quickly evaluated to support efficient NN candidate location. We design a trinary-projection direction-based partition function. The trinary-projection direction is defined as a combination of a few coordinate axes with the weights being 1 or -1. We pursue the projection direction using the widely adopted maximum variance criterion to guarantee good space partitioning and find fewer coordinate axes to guarantee efficient partition function evaluation. We present a coordinate-wise enumeration algorithm to find the principal trinary-projection direction. In addition, we provide an extension using multiple randomized trees for improved performance. We justify our approach on large-scale local patch indexing and similar image search.

In this paper, we investigate the problem of identifying influential users in mobile social networks. Influential users are individuals with high centrality in their social-contact graphs. Traditional approaches find these users through centralized algorithms. However, the computational complexity of these algorithms is known to be very high, making them unsuitable for large-scale networks. We propose a lightweight and distributed protocol, iWander, to identify influential users through fixed-length random-walk sampling. We prove that random-walk sampling with O(logn) steps, where n is the number of nodes in a graph, comes quite close to sampling vertices approximately according to their degrees. To the best of our knowledge, we are the first to design a distributed protocol on mobile devices that leverages random walks for identifying influential users, although this technique has been used in other areas. The most attractive feature of iWander is its extremely low control-message overhead, which lends itself well to mobile applications. We evaluate the performance of iWander for two applications, targeted immunization of infectious diseases and target-set selection for information dissemination. Through extensive simulation studies using a real-world mobility trace, we demonstrate that targeted immunization using iWander achieves a comparable performance with a degree-based immunization policy that vaccinates users with a large number of contacts first, while generating only less than 1% of this policy's control messages. We also show that target-set selection based on iWander outperforms the random and degree-based selections for information dissemination in several scenarios.

We consider the following document ranking problem: We have a collection of documents, each containing some topics (e.g. sports, politics, economics). We also have a set of users with diverse interests. Assume that user u is interested in a subset I_u of topics. Each user u is also associated with a positive integer K_u, which indicates that u can be satisfied by any K_u topics in I_u. Each document s contains information for a subset C_s of topics. The objective is to pick one document at a time such that the average satisfying time is minimized, where a user's satisfying time is the first time that at least K_u topics in I_u are covered in the documents selected so far. Our main result is an O(rho)-approximation algorithm for the problem, where rho is the algorithmic integrality gap of the linear programming relaxation of the set cover instance defined by the documents and topics. This result generalizes the constant approximations for generalized min-sum set cover and ranking with unrelated intents and the logarithmic approximation for the problem of ranking with submodular valuations (when the submodular function is the coverage function), and can be seen as an interpolation between these results. We further extend our model to the case when each user may be interested in more than one sets of topics and when the user's valuation function is XOS, and obtain similar results for these models.

We study several stochastic combinatorial problems, including the expected utility maximization problem, the stochastic knapsack problem and the stochastic bin packing problem. A common technical challenge in these problems is to optimize some function (other than the expectation) of the sum of a set of random variables. The difficulty is mainly due to the fact that the probability distribution of the sum is the convolution of a set of distributions, which is not an easy objective function to work with. To tackle this difficulty, we introduce the Poisson approximation technique. The technique is based on the Poisson approximation theorem discovered by Le Cam, which enables us to approximate the distribution of the sum of a set of random variables using a compound Poisson distribution. Using the technique, we can reduce a variety of stochastic problems to the corresponding deterministic multiple-objective problems, which either can be solved by standard dynamic programming or have known solutions in the literature. For the problems mentioned above, we obtain the following results: We first study the expected utility maximization problem introduced recently [Li and Despande, FOCS11]. For monotone and Lipschitz utility functions, we obtain an additive PTAS if there is a multidimensional PTAS for the multi-objective version of the problem, strictly generalizing the previous result. The result implies the first additive PTAS for maximizing threshold probability for the stochastic versions of global min-cut, matroid base and matroid intersection. For the stochastic bin packing problem (introduced in [Kleinberg, Rabani and Tardos, STOC97]), we show there is a polynomial time algorithm which uses at most the optimal number of bins, if we relax the size of each bin and the overflow probability by e for any constant ε>0. Based on this result, we obtain a 3-approximation if only the size of each bin can be relaxed by ε, improving the known O(1/ε) factor for constant overflow probability. For stochastic knapsack, we show a (1+ε)-approximation using ε extra capacity for any ε>0, even when the size and reward of each item may be correlated and cancelations of items are allowed. This generalizes the previous work [Balghat, Goel and Khanna, SODA11] for the case without correlation and cancelation. Our algorithm is also simpler. We also present a factor 2+ε approximation algorithm for stochastic knapsack with cancelations, for any constant ε>0, improving the current known approximation factor of 8 [Gupta, Krishnaswamy, Molinaro and Ravi, FOCS11]. We also study an interesting variant of the stochastic knapsack problem, where the size and the profit of each item are revealed before the decision is made. The problem falls into the framework of Bayesian online selection problems, which has been studied a lot recently.

Tabular data on the Web has become a rich source of structured data that is useful for ordinary users to explore. Due to its potential, tables on the Web have recently attracted a number of studies with the goals of understanding the semantics of those Web tables and providing effective search and exploration mechanisms over them. An important part of table understanding and search is column concept determination, i.e., identifying the most appropriate concepts associated with the columns of the tables. The problem becomes especially challenging with the availability of increasingly rich knowledge bases that contain hundreds of millions of entities. In this paper, we focus on an important instantiation of the column concept determination problem, namely, the concepts of a column are determined by fuzzy matching its cell values to the entities within a large knowledge base. We provide an efficient and scalable MapReduce-based solution that is scalable to both the number of tables and the size of the knowledge base and propose two novel techniques: knowledge concept aggregation and knowledge entity partition. We prove that both the problem of finding the optimal aggregation strategy and that of finding the optimal partition strategy are NP-hard, and propose efficient heuristic techniques by leveraging the hierarchy of the knowledge base. Experimental results on real-world datasets show that our method achieves high annotation quality and performance, and scales well.

Abstract Problems dealing with assignment of clients to servers have been widely studied. However, they usually do not model the fact that the delay incurred by a client is a function of both the distance to the assigned server and the load on this server, under a given assignment. We study a problem referred to as the load‐distance balancing (LDB) problem, where the objective is assigning a set of clients to a set of given servers. Each client suffers a delay, that is, the sum of the network delay (which is proportional to the distance to its server) and the congestion delay at this server, a nondecreasing function of the number of clients assigned to the server. We address two flavors of LDB—the first one seeking to minimize the maximum incurred delay, and the second one targeted for minimizing the average delay. For the first variation, we present hardness results, a best possible approximation algorithm, and an optimal algorithm for a special case of linear placement of clients and servers. For the second one, we show the problem is NP‐hard in general, and present a 2‐approximation for concave delay functions and an exact algorithm, if the delay function is convex. We also consider the game theoretic version of the second problem and show the price of stability of the game is at most 2 and at least 4/3. © 2011 Wiley Periodicals, Inc. NETWORKS, 2012

We study the stochastic versions of a broad class of combinatorial problems where the weights of the elements in the input dataset are uncertain. The class of problems that we study includes shortest paths, minimum weight spanning trees, and minimum weight matchings over probabilistic graphs, and other combinatorial problems like knapsack. We observe that the expected value is inadequate in capturing different types of risk averse or risk-prone behaviors, and instead we consider a more general objective which is to maximize the expected utility of the solution for some given utility function, rather than the expected weight (expected weight becomes a special case). We show that we can obtain a polynomial time approximation algorithm with additive error ϵ for any ϵ >; 0, if there is a pseudopolynomial time algorithm for the exact version of the problem (This is true for the problems mentioned above) and the maximum value of the utility function is bounded by a constant. Our result generalizes several prior results on stochastic shortest path, stochastic spanning tree, and stochastic knapsack. Our algorithm for utility maximization makes use of the separability of exponential utility and a technique to decompose a general utility function into exponential utility functions, which may be useful in other stochastic optimization problems.

We study the problem of generating synthetic databases having declaratively specified characteristics. This problem is motivated by database system and application testing, data masking, and benchmarking. While the data generation problem has been studied before, prior approaches are either non-declarative or have fundamental limitations relating to data characteristics that they can capture and efficiently support. We argue that a natural, expressive, and declarative mechanism for specifying data characteristics is through cardinality constraints; a cardinality constraint specifies that the output of a query over the generated database have a certain cardinality. While the data generation problem is intractable in general, we present efficient algorithms that can handle a large and useful class of constraints. We include a thorough empirical evaluation illustrating that our algorithms handle complex constraints, scale well as the number of constraints increase, and outperform applicable prior techniques.

Probabilistic database systems have successfully established themselves as a tool for managing uncertain data. However, much of the research in this area has focused on efficient query evaluation and has largely ignored two key issues that commonly arise in uncertain data management: First, how to provide explanations for query results, e.g., Why is this tuple in my result? or Why does this output tuple have such high probability?. Second, the problem of determining the sensitive input tuples for the given query, e.g., users are interested to know the input tuples that can substantially alter the output, when their probabilities are modified (since they may be unsure about the input probability values). Existing systems provide the lineage/provenance of each of the output tuples in addition to the output probabilities, which is a boolean formula indicating the dependence of the output tuple on the input tuples. However, lineage does not immediately provide a quantitative relationship and it is not informative when we have multiple output tuples. In this paper, we propose a unified framework that can handle both the issues mentioned above to facilitate robust query processing. We formally define the notions of influence and explanations and provide algorithms to determine the top-l influential set of variables and the top-l set of explanations for a variety of queries, including conjunctive queries, probabilistic threshold queries, top-k queries and aggregation queries. Further, our framework naturally enables highly efficient incremental evaluation when input probabilities are modified (e.g., if uncertainty is resolved). Our preliminary experimental results demonstrate the benefits of our framework for performing robust query processing over probabilistic databases.

In this paper we consider a generalization of the machine activation problem introduced recently [“Energy efficient scheduling via partial shutdown” by Khuller, Li and Saha (ACM-SIAM 2010 Symp. on Discrete Algorithms)] where the unrelated parallel machine scheduling problem is studied with machine activation cost. This is the standard unrelated parallel machine scheduling problem with a machine dependent activation cost that is incurred, if any job is assigned to the machine. The problem asks for a choice of machines to activate, and a schedule of all jobs on the active machines subject to the makespan constraint. The goal is to minimize the total activation cost. Our main generalization consists of a general activation cost model, where the activation cost for a machine is a non-decreasing function of its load. We develop a greedy algorithm that yields a fractional assignment of jobs, such that at least n − ε jobs are assigned fractionally and the total cost is at most 1 + ln(n/ε) times the optimum. Combining with standard rounding methods yields improved bounds for several machine activation problems. In addition, we study the machine activation problem with d linear constraints (these could model makespan constraints, as well as other types of constraints). Our method yields a schedule with machine activation cost of times the optimum and a constraint violation by a factor of 2d + ε. This result matches our previous bound for the case d = 1. As a by-product, our method also yields a ln n + 1 approximation factor for the non-metric universal facility location problem for which the cost of opening a facility is an arbitrary non-decreasing function of the number of clients assigned to it. This gives an affirmative answer to the open question posed in earlier work on universal facility location.

We address the problem of efficiently gathering correlated data from a wireless sensor network, with the aim of designing algorithms with provable optimality guarantees, and understanding how close we can get to the known theoretical lower bounds. Our proposed approach is based on finding an optimal or a near-optimalcompression treefor a given sensor network: a compression tree is a directed tree over the sensor network nodes such that the value of a node is compressed using the value of its parent. We focus onbroadcast communicationmodel in this paper, but our results are more generally applicable to a unicast communication model as well. We draw connections between the data collection problem and a previously studied graph concept calledweakly connected dominating sets, and we use this to develop novel approximation algorithms for the problem. We present comparative results on several synthetic and real-world datasets showing that our algorithms construct near-optimal compression trees that yield a significant reduction in the data collection cost.

Motivated by issues of saving energy in data centers we define a collection of new problems referred to as “machine activation” problems. The central framework we introduce considers a collection of m machines (unrelated or related) with each machine i having an activation cost of ai. There is also a collection of n jobs that need to be performed, and pi,j is the processing time of job j on machine i. Standard scheduling models assume that the set of machines is fixed and all machines are available. However, in our setting, we assume that there is an activation cost budget of A – we would like to select a subset S of the machines to activate with total cost a(S) ≤ A and find a schedule for the n jobs on the machines in S minimizing the makespan (or any other metric). We consider both the unrelated machines setting, as well as the setting of scheduling uniformly related parallel machines, where machine i has activation cost ai and speed si, and the processing time of job j on machine i is , where pj is the processing requirement of job j. For the general unrelated machine activation problem, our main results are that if there is a schedule with makespan T and activation cost A then we can obtain a schedule with makespan (2 + ε)T and activation cost , for any ε > 0. We also consider assignment costs for jobs as in the generalized assignment problem, and using our framework, provide algorithms that minimize the machine activation and the assignment cost simultaneously. In addition, we present a greedy algorithm which only works for the basic version and yields a makespan of 2T and an activation cost A(1 + ln n). For the uniformly related parallel machine scheduling problem, we develop a polynomial time approximation scheme that outputs a schedule with the property that the activation cost of the subset of machines is at most A and the makespan is at most (1 + ε)T for any ε > 0. For the special case of m identical speed machines, the machine activation problem is trivial, since the cheapest subset of k machines is always the best choice if the optimal solution activates k machines. In addition, we consider the case when some jobs can be dropped (and are treated as outliers).

Ranking is a fundamental operation in data analysis and decision support, and plays an even more crucial role if the dataset being explored exhibits uncertainty. This has led to much work in understanding how to rank uncertain datasets in recent years. In this paper, we address the problem of ranking when the tuple scores are uncertain, and the uncertainty is captured using continuous probability distributions (e.g. Gaussian distributions). We present a comprehensive solution to compute the values of a parameterized ranking function (PRF) [18] for arbitrary continuous probability distributions (and thus rank the uncertain dataset); PRF can be used to simulate or approximate many other ranking functions proposed in prior work. We develop exact polynomial time algorithms for some continuous probability distribution classes, and efficient approximation schemes with provable guarantees for arbitrary probability distributions. Our algorithms can also be used for exact or approximate evaluation of k-nearest neighbor queries over uncertain objects, whose positions are modeled using continuous probability distributions. Our experimental evaluation over several datasets illustrates the effectiveness of our approach at efficiently ranking uncertain datasets with continuous attribute uncertainty.

Increasing prevalence of large-scale distributed monitoring and computing environments such as sensor networks, scientific federations, Grids etc., has led to a renewed interest in the area of distributed query processing and optimization. In this paper we address a general, distributed multi-query processing problem motivated by the need to minimize the communication cost in these environments. Specifically we address the problem of optimally sharing data movement across the communication edges in a distributed communication network given a set of overlapping queries and query plans for them (specifying the operations to be executed). Most of the problem variations of our general problem can be shown to be NP-Hard by a reduction from the Steiner tree problem. However, we show that the problem can be solved optimally if the communication network is a tree, and present a novel algorithm for finding an optimal data movement plan. For general communication networks, we present efficient approximation algorithms for several variations of the problem. Finally, we present an experimental study over synthetic datasets showing both the need for exploiting the sharing of data movement and the effectiveness of our algorithms at finding such plans.

We address the problem of finding a "best" deterministic query answer to a query over a probabilistic database. For this purpose, we propose the notion of a consensus world (or a consensus answer) which is a deterministic world (answer) that minimizes the expected distance to the possible worlds (answers). This problem can be seen as a generalization of the well-studied inconsistent information aggregation problems (e.g. rank aggregation) to probabilistic databases. We consider this problem for various types of queries including SPJ queries, Top-k ranking queries, group-by aggregate queries, and clustering. For different distance metrics, we obtain polynomial time optimal or approximation algorithms for computing the consensus answers (or prove NP-hardness). Most of our results are for a general probabilistic database model, called and/xor tree model, which significantly generalizes previous probabilistic database models like x-tuples and block-independent disjoint models, and is of independent interest.

The dramatic growth in the number of application domains that naturally generate probabilistic, uncertain data has resulted in a need for efficiently supporting complex querying and decision-making over such data. In this paper, we present a unified approach to ranking and top-k query processing in probabilistic databases by viewing it as a multi-criteria optimization problem, and by deriving a set of features that capture the key properties of a probabilistic dataset that dictate the ranked result. We contend that a single, specific ranking function may not suffice for probabilistic databases, and we instead propose two parameterized ranking functions , called PRF ω and PRF e , that generalize or can approximate many of the previously proposed ranking functions. We present novel generating functions -based algorithms for efficiently ranking large datasets according to these ranking functions, even if the datasets exhibit complex correlations modeled using probabilistic and/xor trees or Markov networks . We further propose that the parameters of the ranking function be learned from user preferences, and we develop an approach to learn those parameters. Finally, we present a comprehensive experimental study that illustrates the effectiveness of our parameterized ranking functions, especially PRF e , at approximating other ranking functions and the scalability of our proposed algorithms for exact or approximate ranking.

There is a large literature devoted to the problem of finding an optimal (min-cost) prefix-free code with an unequal letter-cost encoding alphabet of size. While there is no known polynomial time algorithm for solving it optimally, there are many good heuristics that all provide additive errors to optimal. The additive error in these algorithms usually depends linearly upon the largest encoding letter size.

We consider the practical NP-complete problem of finding a minimum weight spanning tree with both edge weights and inner nodes weights. We present two polynomial time algorithms with approximation factors of 2.35 · ln n and 2Hn, respectively, where n is the number of nodes in the graph and Hn is the n-th Harmonic number. This nearly matches the lower bound of (l-\in )Hn, for any \in \ge 0. We also give an approximation algorithm with approximation factor \Delta - 1, where \Delta is the maximum degree of the graph. For metric spaces, we give a 3.105-approximation algorithm and show that an approximation factor of 1.463 is impossible unless {NP \subseteq DTIME[n^{O(\log longn)} ]}.