Enterprise AI Assistants are increasingly deployed in domains where accuracy is paramount, making each erroneous output a potentially significant incident. This paper presents a comprehensive framework for monitoring, benchmarking, and continuously improving such complex, multi-component systems under active development by multiple teams. Our approach encompasses three key elements: (1) a hierarchical ``severity'' framework for incident detection that identifies and categorizes errors while attributing component-specific error rates, facilitating targeted improvements; (2) a scalable and principled methodology for benchmark construction, evaluation, and deployment, designed to accommodate multiple development teams, mitigate overfitting risks, and assess the downstream impact of system modifications; and (3) a continual improvement strategy leveraging multidimensional evaluation, enabling the identification and implementation of diverse enhancement opportunities. By adopting this holistic framework, organizations can systematically enhance the reliability and performance of their AI Assistants, ensuring their efficacy in critical enterprise environments. We conclude by discussing how this multifaceted evaluation approach opens avenues for various classes of enhancements, paving the way for more robust and trustworthy AI systems.

We investigate experimental design for randomized controlled trials (RCTs) with both equal and unequal treatment-control assignment probabilities. Our work makes progress on the connection between the distributional discrepancy minimization (DDM) problem introduced by Harshaw et al. (2024) and the design of RCTs. We make two main contributions: First, we prove that approximating the optimal solution of the DDM problem within a certain constant error is NP-hard. Second, we introduce a new Multiplicative Weights Update (MWU) algorithm for the DDM problem, which improves the Gram-Schmidt walk algorithm used by Harshaw et al. (2024) when assignment probabilities are unequal. Building on the framework of Harshaw et al. (2024) and our MWU algorithm, we then develop the MWU design, which reduces the worst-case mean-squared error in estimating the average treatment effect. Finally, we present a comprehensive simulation study comparing our design with commonly used designs.

Offline reinforcement learning (RL) is a variant of RL where the policy is learned from a previously collected dataset of trajectories and rewards. In our work, we propose a practical approach to offline RL with large language models (LLMs). We recast the problem as reward-weighted fine-tuning, which can be solved using similar techniques to supervised fine-tuning (SFT). To showcase the value of our approach, we apply it to learning short-horizon question-answering policies of a fixed length, where the agent reasons about potential answers or asks clarifying questions. Our work stands in a stark contrast to state-of-the-art methods in this domain, based on SFT and direct preference optimization, which have additional hyper-parameters and do not directly optimize for rewards. We compare to them empirically, and report major gains in both optimized rewards and language quality.

Junda Wu, Tong Yu, Xiang Chen, Haoliang Wang, Ryan Rossi, Sungchul Kim, Anup Rao, Julian McAuley. Proceedings of the 62nd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers). 2024.

Yu Xia, Xu Liu, Tong Yu, Sungchul Kim, Ryan Rossi, Anup Rao, Tung Mai, Shuai Li. Proceedings of the 2024 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies (Volume 1: Long Papers). 2024.

We study oblivious sketching for $k$-sparse linear regression under various loss functions. In particular, we are interested in a distribution over sketching matrices $S\in\mathbb{R}^{m\times n}$ that does not depend on the inputs $A\in\mathbb{R}^{n\times d}$ and $b\in\mathbb{R}^n$, such that, given access to $SA$ and $Sb$, we can recover a $k$-sparse $\tilde x\in\mathbb{R}^d$ with $\|A\tilde x-b\|_f\leq (1+\varepsilon) \min\nolimits_{k{\mathrm{-sparse}\,x\in\mathbb{R}^d}} \|Ax-b\|_f$. Here $\|\cdot\|_f: \mathbb R^n \rightarrow \mathbb R$ is some loss function – such as an $\ell_p$ norm, or from a broad class of hinge-like loss functions, which includes the logistic and ReLU losses. We show that for sparse $\ell_2$ norm regression, there is a distribution over oblivious sketches with $m=\Theta(k\log(d/k)/\varepsilon^2)$ rows, which is tight up to a constant factor. This extends to $\ell_p$ loss with an additional additive $O(k\log(k/\varepsilon)/\varepsilon^2)$ term in the upper bound. This establishes a surprising separation from the related sparse recovery problem, which is an important special case of sparse regression, where $A$ is the identity matrix. For this problem, under the $\ell_2$ norm, we observe an upper bound of $m=O(k \log (d)/\varepsilon + k\log(k/\varepsilon)/\varepsilon^2)$, showing that sparse recovery is strictly easier to sketch than sparse regression. For sparse regression under hinge-like loss functions including sparse logistic and sparse ReLU regression, we give the first known sketching bounds that achieve $m = o(d)$ showing that $m=O(\mu^2 k\log(\mu n d/\varepsilon)/\varepsilon^2)$ rows suffice, where $\mu$ is a natural complexity parameter needed to obtain relative error bounds for these loss functions. We again show that this dimension is tight, up to lower order terms and the dependence on $\mu$. Finally, we show that similar sketching bounds can be achieved for LASSO regression, a popular convex relaxation of sparse regression, where one aims to minimize $\|Ax-b\|_2^2+\lambda\|x\|_1$ over $x\in\mathbb{R}^d$. We show that sketching dimension $m =O(\log(d)/(\lambda \varepsilon)^2)$ suffices and that the dependence on $d$ and $\lambda$ is tight.

There is increasing attention toward search indexes based on dense vector representations as they can encode latent semantic features and can be generated efficiently, thanks to the advances in representation learning. Building an index on vectors was addressed by methods like locality-sensitive hashing (LSH), Inverted File Index (IVF), and near-neighbor graphs and perfected for high performance. However, the current near-neighbor (NN) indexes cannot be directly used in a real recommendation engine where both learned dense features and the constraints-attributes are used. The existing methods are cascaded index with vector search followed by a naive matching or inverted index for filtering on attribute tokens. This filtering on post-vector search matched sets often limits the control on output size and adds latency due to repeated calls to the NN engine. We aim to make a single-stage retrieval model that can retrieve in a single pass and control the output size without compromising on latency. An NN index amenable to this should have a very similar structure to the attribute token-based inverted index. Hence, we develop an efficient constraint search engine based on the high dimensional sparse embeddings of semantic features added with attribute tokens. With this, we get an Inverted index-based Constraint Near Neighbor search-ICONN, where we retrieve search results with 100% match on query attributes and close to its semantic features. We achieve a better latency vs recall10@10 tradeoff compared to the standard NN search followed by attribute filtering.

Vanilla federated learning does not support learning in an online environment, learning a personalized model on each client, and learning in a decentralized setting. There are existing methods extending federated learning in each of the three aspects. However, some important applications on enterprise edge servers (e.g. online item recommendation at global scale) involve the three aspects at the same time. Therefore, we propose a new learning setting Decentralized Personalized Online Federated Learning that considers all the three aspects at the same time.In this new setting for learning, the first technical challenge is how to aggregate the shared model parameters from neighboring clients to obtain a personalized local model with good performance on each client. We propose to directly learn an aggregation by optimizing the performance of the local model with respect to the aggregation weights. This not only improves personalization of each local model but also helps the local model adapting to potential data shift by intelligently incorporating the right amount of information from its neighbors. The second challenge is how to select the neighbors for each client. We propose a peer selection method based on the learned aggregation weights enabling each client to select the most helpful neighbors and reduce communication cost at the same time. We verify the effectiveness and robustness of our proposed method on three real-world item recommendation datasets and one air quality prediction dataset.

Graph models based on factorization of the adjacency matrix often fail to capture network structures related to links between dissimilar nodes (heterophily). We introduce a novel graph factorization model that leverages two nonnegative vectors per node to interpretably account for links between both similar and dissimilar nodes. We prove that our model can exactly represent any graph with low *arboricity*, a property that many real-world networks satisfy; our proof also applies to related models but has much greater scope than the closest prior bound, which is based on low *max degree*. Our factorization also has compelling properties besides expressiveness: due to its symmetric structure and nonnegativity, fitting the model inherently finds node communities, and the model's link predictions can be interpreted in terms of these communities. In experiments on real-world networks, we demonstrate our factorization's effectiveness on a variety of tasks, including community detection and link prediction.

The design and analysis of randomized experiments is fundamental to many areas, from the physical and social sciences to industrial settings. Regression adjustment is a popular technique to reduce the variance of estimates obtained from experiments, by utilizing information contained in auxiliary covariates. While there is a large literature within the statistics community studying various approaches to regression adjustment and their asymptotic properties, little focus has been given to approaches in the finite population setting with non-asymptotic accuracy bounds. Further, prior work typically assumes that an entire population is exposed to an experiment, whereas practitioners often seek to minimize the number of subjects exposed to an experiment, for ethical and pragmatic reasons. In this work, we study the problems of estimating the sample mean, individual treatment effects, and average treatment effect with regression adjustment. We propose approaches that use techniques from randomized numerical linear algebra to sample a subset of the population on which to perform an experiment. We give non-asymptotic accuracy bounds for our methods and demonstrate that they compare favorably with prior approaches.

Several cloud-based applications, such as cloud gaming, rent servers to execute jobs which arrive in an online fashion. Each job has a resource demand, such as GPU requirement, and must be dispatched to a cloud server which has enough resources to execute the job, which departs after its completion. Under the "pay-as-you-go'' billing model, the server rental cost is proportional to the total time that servers are actively running jobs. The problem of efficiently allocating a sequence of online jobs to servers without exceeding the resource capacity of any server while minimizing total server usage time can be modelled as a variant of the dynamic bin packing problem (DBP), called MinUsageTime DBP [10].

The goal of Approximate Query Processing (AQP) is to provide very fast but "accurate enough" results for costly aggregate queries thereby improving user experience in interactive exploration of large datasets. Recently proposed Machine-Learning-based AQP techniques can provide very low latency as query execution only involves model inference as compared to traditional query processing on database clusters. However, with increase in the number of filtering predicates (WHERE clauses), the approximation error significantly increases for these methods. Analysts often use queries with a large number of predicates for insights discovery. Thus, maintaining low approximation error is important to prevent analysts from drawing misleading conclusions. In this paper, we propose ELECTRA, a predicate-aware AQP system that can answer analytics-style queries with a large number of predicates with much smaller approximation errors. ELECTRA uses a conditional generative model that learns the conditional distribution of the data and at run-time generates a small (≈ 1000 rows) but representative sample, on which the query is executed to compute the approximate result. Our evaluations with four different baselines on three real-world datasets show that ELECTRA provides lower AQP error for large number of predicates compared to baselines.

We consider the experimental design problem in an online environment, an important practical task for reducing the variance of estimates in randomized experiments which allows for greater precision, and in turn, improved decision making. In this work, we present algorithms that build on recent advances in online discrepancy minimization which accommodate both arbitrary treatment probabilities and multiple treatments. The proposed algorithms are computational efficient, minimize covariate imbalance, and include randomization which enables robustness to misspecification. We provide worst case bounds on the expected mean squared error of the causal estimate and show that the proposed estimator is no worse than an implicit ridge regression, which are within a logarithmic factor of the best known results for offline experimental design. We conclude with a detailed simulation study showing favorable results relative to complete randomization as well as to offline methods for experimental design with time complexities exceeding our algorithm, which has a linear dependence on the number of observations, by polynomial factors.

In this paper, we initiate the study of one-pass algorithms for solving the maximum-a-posteriori (MAP) inference problem for Non-symmetric Determinantal Point Processes (NDPPs). In particular, we formulate streaming and online versions of the problem and provide one-pass algorithms for solving these problems. In our streaming setting, data points arrive in an arbitrary order and the algorithms are constrained to use a single-pass over the data as well as sub-linear memory, and only need to output a valid solution at the end of the stream. Our online setting has an additional requirement of maintaining a valid solution at any point in time. We design new one-pass algorithms for these problems and show that they perform comparably to (or even better than) the offline greedy algorithm while using substantially lower memory.

Treatment effect estimation is a fundamental problem in causal inference. We focus on designing efficient randomized controlled trials, to accurately estimate the effect of some treatment on a population of $n$ individuals. In particular, we study \textit{sample-constrained treatment effect estimation}, where we must select a subset of $s \ll n$ individuals from the population to experiment on. This subset must be further partitioned into treatment and control groups. Algorithms for partitioning the entire population into treatment and control groups, or for choosing a single representative subset, have been well-studied. The key challenge in our setting is jointly choosing a representative subset and a partition for that set. We focus on both individual and average treatment effect estimation, under a linear effects model. We give provably efficient experimental designs and corresponding estimators, by identifying connections to discrepancy minimization and leverage-score-based sampling used in randomized numerical linear algebra. Our theoretical results obtain a smooth transition to known guarantees when $s$ equals the population size. We also empirically demonstrate the performance of our algorithms.

There are various scenarios where very quick insights from a massive amount of data need to be extracted in a time-critical manner. These might be fresh insights or re-looking at why previous insights did not work and how to fix those. A marketing campaign is one real-world scenario where a non-programmer needs to dig such huge data in a very short period of time (a few hours) in order to hit a target revenue. In this demo paper, we will describe Electra - a system that integrates an automated data-insight discovery mechanism with a novel machine-learning (ML) driven approximate query processing (AQP) engine that can answer complex queries with a large number of predicates or conditions with high accuracy. This AQP engine uses a conditional generative model to generate a very small sample (~1000 rows) corresponding to the actual query to be answered and computes the highly accurate approximate answer from those instead of running the query against the original data. The insight discovery workflow bootstraps insights using ML algorithms based on the statistical characteristics of the data and further offers a no-code based interface to drill down for deeper insights. The queries from this interface are answered by the AQP engine that runs locally at the client-side itself to offer low latency interactions.

Graph Neural Networks (GNNs) have proven to be useful for many different practical applications. However, many existing GNN models have implicitly assumed homophily among the nodes connected in the graph, and therefore have largely overlooked the important setting of heterophily, where most connected nodes are from different classes. In this work, we propose a novel framework called CPGNN that generalizes GNNs for graphs with either homophily or heterophily. The proposed framework incorporates an interpretable compatibility matrix for modeling the heterophily or homophily level in the graph, which can be learned in an end-to-end fashion, enabling it to go beyond the assumption of strong homophily. Theoretically, we show that replacing the compatibility matrix in our framework with the identity (which represents pure homophily) reduces to GCN. Our extensive experiments demonstrate the effectiveness of our approach in more realistic and challenging experimental settings with significantly less training data compared to previous works: CPGNN variants achieve state-of-the-art results in heterophily settings with or without contextual node features, while maintaining comparable performance in homophily settings.

In this work, we address the problem of balanced treatment assignment for experiments by considering an interpretation of the problem as optimization of a two-sample test between test and control units. Using this lens we provide an assignment algorithm that is optimal with respect to the minimum spanning tree test of Friedman and Rafsky [1979]. This assignment to treatment groups may be performed exactly in polynomial time and allows for the design of experiments explicitly targeting the individual treatment effect. We provide a probabilistic interpretation of this process in terms of the most probable element of designs drawn from a determinantal point process. We provide a novel formulation of estimation as transductive inference and show how the tree structures used in design can also be used in an adjustment estimator. We conclude with a simulation study demonstrating the improved efficacy of our method.

We consider the problem of designing a randomized experiment on a source population to estimate the Average Treatment Effect (ATE) on a target population. We propose a novel approach which explicitly considers the target when designing the experiment on the source. Under the covariate shift assumption, we design an unbiased importance-weighted estimator for the target population’s ATE. To reduce the variance of our estimator, we design a covariate balance condition (Target Balance) between the treatment and control groups based on the target population. We show that Target Balance achieves a higher variance reduction asymptotically than methods that do not consider the target population during the design phase. Our experiments illustrate that Target Balance reduces the variance even for small sample sizes.

This paper introduces higher-order link prediction methods based on the notion of closing higher-order network motifs. The methods are fast and efficient for real-time ranking and link prediction-based applications such as online visitor stitching, web search, and online recommendation. In such applications, real-time performance is critical. The proposed methods do not require any explicit training data, nor do they derive an embedding from the graph data, or perform any explicit learning. Most existing unsupervised methods with the above desired properties are all based on closing triangles (common neighbors, Jaccard similarity, and the ilk). In this work, we develop unsupervised techniques based on the notion of closing higher-order motifs that generalize beyond closing simple triangles. Through extensive experiments, we find that these higher-order motif closures often outperform triangle-based methods, which are commonly used in practice. This result implies that one should consider other motif closures beyond simple triangles. We also find that the best motif closure depends highly on the underlying network and its structural properties. Furthermore, all methods described in this work are fast for link prediction-based applications requiring real-time performance. The experimental results indicate the importance of closing higher-order motifs for unsupervised link prediction. Finally, these new higher-order motif closures can serve as a basis for studying and developing better unsupervised real-time link prediction and ranking methods.

We study the problem of machine unlearning and identify a notion of algorithmic stability, Total Variation (TV) stability, which we argue, is suitable for the goal of exact unlearning. For convex risk minimization problems, we design TV-stable algorithms based on noisy Stochastic Gradient Descent (SGD). Our key contribution is the design of corresponding efficient unlearning algorithms, which are based on constructing a near-maximal coupling of Markov chains for the noisy SGD procedure. To understand the trade-offs between accuracy and unlearning efficiency, we give upper and lower bounds on excess empirical and populations risk of TV stable algorithms for convex risk minimization. Our techniques generalize to arbitrary non-convex functions, and our algorithms are differentially private as well.

Adversarial training is among the most effective techniques to improve robustness of models against adversarial perturbations. However, the full effect of this approach on models is not well understood. For example, while adversarial training can reduce the adversarial risk (prediction error against an adversary), it sometimes increase standard risk (generalization error when there is no adversary). In this paper, we focus on \emph{distribution perturbing} adversary framework wherein the adversary can change the test distribution within a neighborhood of the training data distribution. The neighborhood is defined via Wasserstein distance between distributions and the radius of the neighborhood is a measure of adversary’s manipulative power. We study the tradeoff between standard risk and adversarial risk and derive the Pareto-optimal tradeoff, achievable over specific classes of models, in the infinite data limit with features dimension kept fixed. We consider three learning settings: 1) Regression with the class of linear models; 2) Binary classification under the Gaussian mixtures data model, with the class of linear classifiers; 3) Regression with the class of random features model (which can be equivalently represented as two-layer neural network with random first-layer weights). We show that a tradeoff between standard and adversarial risk is manifested in all three settings. We further characterize the Pareto-optimal tradeoff curves and discuss how a variety of factors, such as features correlation, adversary’s power or the width of two-layer neural network would affect this tradeoff.

Understanding generalization and estimation error of estimators for simple models such as linear and generalized linear models has attracted a lot of attention recently. This is in part due to an interesting observation made in machine learning community that highly over-parameterized neural networks achieve zero training error, and yet they are able to generalize well over the test samples. This phenomenon is captured by the so called double descent curve, where the generalization error starts decreasing again after the interpolation threshold. A series of recent works tried to explain such phenomenon for simple models. In this work, we analyze the asymptotics of estimation error in ridge estimators for convolutional linear models. These convolutional inverse problems, also known as deconvolution, naturally arise in different fields such as seismology, imaging, and acoustics among others. Our results hold for a large class of input distributions that include i.i.d. features as a special case. We derive exact formulae for estimation error of ridge estimators that hold in a certain high-dimensional regime. We show the double descent phenomenon in our experiments for convolutional models and show that our theoretical results match the experiments.

Online marketing platforms often store millions of website visitors' behavior as a large sparse matrix with rows as visitors and columns as behavior. These platforms allow marketers to conduct Audience Expansion, a technique to identify new audiences with similar behavior to the original target audiences. In this paper, we propose a method to achieve interactive Audience Expansion from millions of visitor data efficiently. Unlike other methods that undergo significant computations upon inputs, our approach provides interactive responses when a marketer inputs the target audiences and similarity measures. The idea is to apply data summarization technique on the large visitor matrix to obtain a small set of summaries representing the similarities in the matrix. We propose efficient algorithms to compute the data summaries on a distributed computing environment (i.e., Spark) and conduct the expansion using the summaries. Our experiment shows that our approach (1) provides 10 times more accurate and 27 times faster Audience Expansion results on real datasets and (2) achieves a 98% speed-up compared to straightforward data summarization implementations. We also present an interface to apply the algorithm for real-world scenarios.

We give relative error coresets for training linear classifiers with a broad class of loss functions, including the logistic loss and hinge loss. Our construction achieves $(1\pm \epsilon)$ relative error with $\tilde O(d \cdot \mu_y(X)^2/\epsilon^2)$ points, where $\mu_y(X)$ is a natural complexity measure of the data matrix $X \in \mathbb{R}^{n \times d}$ and label vector $y \in \{-1,1\}^n$, introduced by Munteanu et al. 2018. Our result is based on subsampling data points with probabilities proportional to their $\ell_1$ $Lewis$ $weights$. It significantly improves on existing theoretical bounds and performs well in practice, outperforming uniform subsampling along with other importance sampling methods. Our sampling distribution does not depend on the labels, so can be used for active learning. It also does not depend on the specific loss function, so a single coreset can be used in multiple training scenarios.

In this article, we introduce a generalization of graphlets to heterogeneous networks called typed graphlets . Informally, typed graphlets are small typed induced subgraphs. Typed graphlets generalize graphlets to rich heterogeneous networks as they explicitly capture the higher-order typed connectivity patterns in such networks. To address this problem, we describe a general framework for counting the occurrences of such typed graphlets. The proposed algorithms leverage a number of combinatorial relationships for different typed graphlets. For each edge, we count a few typed graphlets, and with these counts along with the combinatorial relationships, we obtain the exact counts of the other typed graphlets in o (1) constant time. Notably, the worst-case time complexity of the proposed approach matches the time complexity of the best known untyped algorithm. In addition, the approach lends itself to an efficient lock-free and asynchronous parallel implementation. While there are no existing methods for typed graphlets, there has been some work that focused on computing a different and much simpler notion called colored graphlet. The experiments confirm that our proposed approach is orders of magnitude faster and more space-efficient than methods for computing the simpler notion of colored graphlet. Unlike these methods that take hours on small networks, the proposed approach takes only seconds on large networks with millions of edges. Notably, since typed graphlet is more general than colored graphlet (and untyped graphlets), the counts of various typed graphlets can be combined to obtain the counts of the much simpler notion of colored graphlets. The proposed methods give rise to new opportunities and applications for typed graphlets.

Heterogeneous networks are seemingly ubiquitous in the real world. Yet, most graph mining methods such as clustering have mostly focused on homogeneous graphs by ignoring semantic information in real-world systems. Moreover, most methods are based on first-order connectivity patterns (edges) despite that higher-order connectivity patterns are known to be important in understanding the structure and organization of such networks. In this work, we propose a framework for higher-order spectral clustering in heterogeneous networks through the notions of typed graphlets and typed-graphlet conductance. The proposed method builds clusters that preserve the connectivity of higher-order structures built up from typed graphlets. The approach generalizes previous work on higher-order spectral clustering. We theoretically prove a number of important results including a Cheeger-like inequality for typed-graphlet conductance that shows near-optimal bounds for the method. The theoretical results greatly simplify previous work while providing a unifying theoretical framework for analyzing higher-order spectral methods. Empirically, we demonstrate the effectiveness of the framework quantitatively for three important applications including clustering, compression, and link prediction.

We study bandit model selection in stochastic environments. Our approach relies on a master algorithm that selects between candidate base algorithms. We develop a master-base algorithm abstraction that can work with general classes of base algorithms and different type of adversarial master algorithms. Our methods rely on a novel and generic smoothing transformation for bandit algorithms that permits us to obtain optimal $O(\sqrt{T})$ model selection guarantees for stochastic contextual bandit problems as long as the optimal base algorithm satisfies a high probability regret guarantee. We show through a lower bound that even when one of the base algorithms has $O(\log T)$ regret, in general it is impossible to get better than $\Omega(\sqrt{T})$ regret in model selection, even asymptotically. Using our techniques, we address model selection in a variety of problems such as misspecified linear contextual bandits \citep{lattimore2019learning}, linear bandit with unknown dimension \citep{Foster-Krishnamurthy-Luo-2019} and reinforcement learning with unknown feature maps. Our algorithm requires the knowledge of the optimal base regret to adjust the master learning rate. We show that without such prior knowledge any master can suffer a regret larger than the optimal base regret.

Discrete time event sequences from web users are commonly encountered in a variety of real-world domains, from digital marketing to recommender systems. Most of the literature in the area focuses on supervised prediction tasks of the user's next action or return time. However, little attention has been paid to the challenging task of modeling user evolution and behavior in a quantitative fashion. For example, progress of the users' knowledge in an online tutorial, user exploration, or engagement. We propose methods to perform a time-varying clustering along with event predictions in a unified domain agnostic framework. Our framework can help track the evolution of the users as they interact with the platform. We evaluate our methods on three real-world datasets and show that our method performs at par with the supervised baseline on the prediction tasks while providing meaningful clusters.

In this paper, we study the problem of finding a maximum matching in the semi-streaming model when edges arrive in a random order. In the semi-streaming model, an algorithm receives a stream of edges and it is allowed to have a memory of Õ(n)1 where n is the number of vertices in the graph. A recent inspiring work by Assadi et al. [1] shows that there exists a streaming algorithm with the approximation ratio of ⅔ that uses Õ(n1.5) memory. However, the memory of their algorithm is much larger than the memory constraint of the semi-streaming algorithms. In this work, we further investigate this problem in the semi-streaming model, and we present simple and clean algorithms for approximating maximum matching in the semi-streaming model. Our main results are as follows. We show that there exists a single-pass deterministic semi-streaming algorithm that finds a approximation of the maximum matching in bipartite graphs using Õ(n) memory. This result significantly outperforms the state-of-the-art result of Konrad [12] that finds a 0.539 approximation of the maximum matching using Õ(n) memory. By giving a black-box reduction from finding a matching in general graphs to finding a matching in bipartite graphs, we show there exists a single-pass deterministic semi-streaming algorithm that finds a (≈ 0.545) approximation of the maximum matching in general graphs, improving upon the state-of-art result 0.506 approximation by Gamlath et al. [8].

The success of many graph-based machine learning tasks highly depends on an appropriate representation learned from the graph data. Most work has focused on learning node embeddings that preserve proximity as opposed to structural role-based embeddings that preserve the structural similarity among nodes. These methods fail to capture higher-order structural dependencies and connectivity patterns that are crucial for structural role-based applications such as visitor stitching from web logs. In this work, we formulate higher-order network representation learning and describe a general framework called HONE for learning such structural node embeddings from networks via the subgraph patterns (network motifs, graphlet orbits/positions) in a nodes neighborhood. A general diffusion mechanism is introduced in HONE along with a space-efficient approach that avoids explicit construction of the k-step motif-based matrices using a k-step linear operator. Furthermore, HONE is shown to be fast and efficient with a worst-case time complexity that is nearly-linear in the number of edges. The experiments demonstrate the effectiveness of HONE for a number of important tasks including link prediction and visitor stitching from large web log data.

Online visitor behaviors are often modeled as a large sparse matrix, where rows represent visitors and columns represent behavior. To discover customer segments with different hierarchies, marketers often need to cluster the data in different splits. Such analyses require the clustering algorithm to provide real-time responses on user parameter changes, which the current techniques cannot support. In this paper, we propose a real-time clustering algorithm, sparse density peaks, for large-scale sparse data. It pre-processes the input points to compute annotations and a hierarchy for cluster assignment. While the assignment is only a single scan of the points, a naive pre-processing requires measuring all pairwise distances, which incur a quadratic computation overhead and is infeasible for any moderately sized data. Thus, we propose a new approach based on MinHash and LSH that provides fast and accurate estimations. We also describe an efficient implementation on Spark that addresses data skew and memory usage. Our experiments show that our approach (1) provides a better approximation compared to a straightforward MinHash and LSH implementation in terms of accuracy on real datasets, (2) achieves a 20 × speedup in the end-to-end clustering pipeline, and (3) can maintain computations with a small memory. Finally, we present an interface to explore customer segments from millions of online visitor records in real-time.

We show that variants of spectral sparsification routines can preserve the total spanning tree counts of graphs. By Kirchhoff's matrix-tree theorem, this is equivalent to preserving the determinant of a graph Laplacian minor or, equivalently, of any symmetric diagonally dominant matrix (SDDM). Our analyses utilize this combinatorial connection to bridge the gap between statistical leverage scores/effective resistances and the analysis of random graphs by Janson [ Combin. Probab. Comput., 3 (1994), pp. 97--126]. This leads to a routine that, in quadratic time, sparsifies a graph down to about $n^{1.5}$ edges in a way that preserves both the determinant and the distribution of spanning trees (provided the sparsified graph is viewed as a random object). Extending this algorithm to work with Schur complements and approximate Choleksy factorizations leads to algorithms for counting and sampling spanning trees which are nearly optimal for dense graphs. We give an algorithm that computes a $(1 \pm \delta)$ approximation to the determinant of any SDDM matrix with constant probability in about $n^2 \delta^{-2}$ time. This is the first routine for graphs that outperforms general-purpose routines for computing determinants of arbitrary matrices. We also give an algorithm that generates, in about $n^2 \delta^{-2}$ time, a spanning tree of a weighted undirected graph from a distribution with a total variation distance of $\delta$ from the $\boldsymbol{\mathit{w}}$-uniform distribution.

We study sample complexity of optimizing “hill-climbing friendly” functions defined on a graph under noisy observations. We define a notion of convexity, and we show that a variant of best-arm identification can find a near-optimal solution after a small number of queries that is independent of the size of the graph. For functions that have local minima and are nearly convex, we show a sample complexity for the classical simulated annealing under noisy observations. We show effectiveness of the greedy algorithm with restarts and the simulated annealing on problems of graph-based nearest neighbor classification as well as a web advertising application.

The success of deep convolutional neural networks in the domains of computer vision and speech recognition has led researchers to investigate generalizations of the said architecture to graph-structured data. A recently-proposed method called Graph Convolutional Networks has been able to achieve state-of-the-art results in the task of node classification. However, since the proposed method relies on localized first-order approximations of spectral graph convolutions, it is unable to capture higher-order interactions between nodes in the graph. In this work, we propose a motif-based graph attention model, called Motif Convolutional Networks, which generalizes past approaches by using weighted multi-hop motif adjacency matrices to capture higher-order neighborhoods. A novel attention mechanism is used to allow each individual node to select the most relevant neighborhood to apply its filter. We evaluate our approach on graphs from different domains (social networks and bioinformatics) with results showing that it is able to outperform a set of competitive baselines on the semi-supervised node classification task. Additional results demonstrate the usefulness of attention, showing that different higher-order neighborhoods are prioritized by different kinds of nodes.

Motivated by the computational and storage challenges that dense embeddings pose, we introduce the problem of latent network summarization that aims to learn a compact, latent representation of the graph structure with dimensionality that is independent of the input graph size (\i.e., #nodes and #edges), while retaining the ability to derive node representations on the fly. We propose Multi-LENS, an inductive multi-level latent network summarization approach that leverages a set of relational operators and relational functions (compositions of operators) to capture the structure of egonets and higher-order subgraphs, respectively. The structure is stored in low-rank, size-independent structural feature matrices, which along with the relational functions comprise our latent network summary. Multi-LENS is general and naturally supports both homogeneous and heterogeneous graphs with or without directionality, weights, attributes or labels. Extensive experiments on real graphs show 3.5-34.3% improvement in AUC for link prediction, while requiring 80-2152x less output storage space than baseline embedding methods on large datasets. As application areas, we show the effectiveness of Multi-LENS in detecting anomalies and events in the Enron email communication graph and Twitter co-mention graph.

In this paper, we show how to solve directed Laplacian systems in nearly-linear time. Given a linear system in an n × n Eulerian directed Laplacian with m nonzero entries, we show how to compute an ε-approximate solution in time O(m logO(1)(n) log (1/ε)). Through reductions from [Cohen et al. FOCS'16], this gives the first nearly-linear time algorithms for computing ε-approximate solutions to row or column diagonally dominant linear systems (including arbitrary directed Laplacians) and computing ε-approximations to various properties of random walks on directed graphs, including stationary distributions, personalized PageRank vectors, hitting times, and escape probabilities. These bounds improve upon the recent almost-linear algorithms of [Cohen et al. STOC'17], which gave an algorithm to solve Eulerian Laplacian systems in time O((m+n2O(√ log n log log n))logO(1)(n ε-1)). To achieve our results, we provide a structural result that we believe is of independent interest. We show that Eulerian Laplacians (and therefore the Laplacians of all strongly connected directed graphs) have sparse approximate LU-factorizations. That is, for every such directed Laplacian there are lower upper triangular matrices each with at most Õ(n) nonzero entries such that there product spectrally approximates the directed Laplacian in an appropriate norm. This claim can be viewed as an analog of recent work on sparse Cholesky factorizations of Laplacians of undirected graphs. We show how to construct such factorizations in nearly-linear time and prove that once constructed they yield nearly-linear time algorithms for solving directed Laplacian systems.

We show variants of spectral sparsification routines can preserve the total spanning tree counts of graphs, which by Kirchhoff's matrix-tree theorem, is equivalent to determinant of a graph Laplacian minor, or equivalently, of any SDDM matrix. Our analyses utilizes this combinatorial connection to bridge between statistical leverage scores/effective resistances and the analysis of random graphs by [Janson, Combinatorics, Probability and Computing `94]. This leads to a routine that in quadratic time, sparsifies a graph down to about n1.5 edges in ways that preserve both the determinant and the distribution of spanning trees (provided the sparsified graph is viewed as a random object). Extending this algorithm to work with Schur complements and approximate Cholesky factorizations leads to algorithms for counting and sampling spanning trees which are nearly optimal for dense graphs. We give an algorithm that computes a (1±δ) approximation to the determinant of any SDDM matrix with constant probability in about n2δ-2time. This is the first routine for graphs that outperforms general-purpose routines for computing determinants of arbitrary matrices. We also give an algorithm that generates in about n2δ-2time a spanning tree of a weighted undirected graph from a distribution with total variation distance of δ from the w-uniform distribution.

In this paper, we begin to address the longstanding algorithmic gap between general and reversible Markov chains. We develop directed analogues of several spectral graph-theoretic tools that had previously been available only in the undirected setting, and for which it was not clear that directed versions even existed. In particular, we provide a notion of approximation for directed graphs, prove sparsifiers under this notion always exist, and show how to construct them in almost linear time. Using this notion of approximation, we design the first almost-linear-time directed Laplacian system solver, and, by leveraging the recent framework of [Cohen-Kelner-Peebles-Peng-Sidford-Vladu, FOCS '16], we also obtain almost-linear-time algorithms for computing the stationary distribution of a Markov chain, computing expected commute times in a directed graph, and more. For each problem, our algorithms improve the previous best running times of O((nm3/4 + n2/3 m) logO(1) (n κ ε-1)) to O((m + n2O(√lognloglogn)) logO(1) (n κε-1)) where n is the number of vertices in the graph, m is the number of edges, κ is a natural condition number associated with the problem, and ε is the desired accuracy. We hope these results open the door for further studies into directed spectral graph theory, and that they will serve as a stepping stone for designing a new generation of fast algorithms for directed graphs.

We present an algorithm that, with high probability, generates a random spanning tree from an edge-weighted undirected graph in (n5/3 m1/3) time. The tree is sampled from a distribution where the probability of each tree is proportional to the product of its edge weights. This improves upon the previous best algorithm due to Colbourn et al. that runs in matrix multiplication time, O(nω). For the special case of unweighted graphs, this improves upon the best previously known running time of Õ(min{nω,m√n,m4/3}) for m ⪢ n7/4 (Colbourn et al. '96, Kelner-Madry '09, Madry et al. '15).

We consider the problem of estimating the mean and covariance of a distribution from i.i.d. samples in the presence of a fraction of malicious noise. This is in contrast to much recent work where the noise itself is assumed to be from a distribution of known type. The agnostic problem includes many interesting special cases, e.g., learning the parameters of a single Gaussian (or finding the best-fit Gaussian) when a fraction of data is adversarially corrupted, agnostically learning mixtures, agnostic ICA, etc. We present polynomial-time algorithms to estimate the mean and covariance with error guarantees in terms of information-theoretic lower bounds. As a corollary, we also obtain an agnostic algorithm for Singular Value Decomposition.

In this paper, we present and analyze a simple and robust spectral algorithm for the stochastic block model with k blocks, for any k fixed. Our algorithm works with graphs having constant edge density, under an optimal condition on the gap between the density inside a block and the density between the blocks. As a co-product, we settle an open question posed by Abbe et. al. concerning censor block models.

We develop fast algorithms for solving regression problems on graphs where one is given the value of a function at some vertices, and must find its smoothest possible extension to all vertices. The extension we compute is the absolutely minimal Lipschitz extension, and is the limit for large p of p-Laplacian regularization. We present an algorithm that computes a minimal Lipschitz extension in expected linear time, and an algorithm that computes an absolutely minimal Lipschitz extension in expected time \widetildeO (m n). The latter algorithm has variants that seem to run much faster in practice. These extensions are particularly amenable to regularization: we can perform l_0-regularization on the given values in polynomial time and l_1-regularization on the initial function values and on graph edge weights in time \widetildeO (m^3/2). Our definitions and algorithms naturally extend to directed graphs.

Given a directed acyclic graph $G,$ and a set of values $y$ on the vertices, the Isotonic Regression of $y$ is a vector $x$ that respects the partial order described by $G,$ and minimizes $\|x-y\|,$ for a specified norm. This paper gives improved algorithms for computing the Isotonic Regression for all weighted $\ell_{p}$-norms with rigorous performance guarantees. Our algorithms are quite practical, and their variants can be implemented to run fast in practice.

We show an algorithm for solving symmetric diagonally dominant (SDD) linear systems with m non-zero entries to a relative error of ε in O(m log1/2 n logc n log(1/ε)) time. Our approach follows the recursive preconditioning framework, which aims to reduce graphs to trees using iterative methods. We improve two key components of this framework: random sampling and tree embeddings. Both of these components are used in a variety of other algorithms, and our approach also extends to the dual problem of computing electrical flows.