From expert AI systems of the 1970s to self-supervised systems of the 2020s, the pendulum of AI development has swung from heavy reliance on human feedback to no or minimal reliance in the last 50 years. Self-supervised approaches have contributed significantly to the success and scalable development of AI. However, today we are at a tipping point where the future of AI, and whether so-ciety ends up benefiting from this technology in the long run, depends critically on the subsequent AI develop-ment aligning with human goals and values. Realizing this, there has been ramping up of efforts to align AI models with human expectations and values. Human feedback, however, remains limited and difficult to elicit. Thus, a key question lingers – how can we scale up alignment of AI systems with individual expectations and societal norms? This talk and paper provides an overview and perspective on efforts at answering this question.

Estimation of the Average Treatment Effect (ATE) is a core problem in causal inference with strong connections to Off-Policy Evaluation in Reinforcement Learning. This paper considers the problem of adaptively selecting the treatment allocation probability in order to improve estimation of the ATE. The majority of prior work on adaptive ATE estimation focus on asymptotic guarantees, and in turn overlooks important practical considerations such as the difficulty of learning the optimal treatment allocation as well as hyper-parameter selection. Existing non-asymptotic methods are limited by poor empirical performance and exponential dependence on problem parameters. In order to address these gaps, we propose and analyze the Clipped Second Moment Tracking (ClipSMT) algorithm, a variant of an existing algorithm with strong asymptotic optimality guarantees, and provide finite sample bounds on its Neyman regret. Our analysis shows that, in the superpopulation setting, ClipSMT achieves exponential improvements in Neyman regret on two fronts: improving the dependence on $T$ from $O(\sqrt{T})$ to $O(\log T)$, as well as reducing the exponential dependence on problem parameters to a polynomial dependence—although the setting we consider is slightly less general. We conclude with simulations which show the marked improvement of ClipSMT over existing approaches.

Randomized controlled trials (RCTs) generate guarantees for treatment effects. However, RCTs often spend unnecessary resources exploring sub-optimal treatments, which can reduce the power of treatment guarantees. To address this, we propose a two-stage RCT design. In the first stage, a data-driven screening procedure prunes low-impact treatments, while the second stage focuses on developing high-probability lower bounds for the best-performing treatment effect. Unlike existing adaptive RCT frameworks, our method is simple enough to be implemented in scenarios with limited adaptivity. We derive optimal designs for two-stage RCTs and demonstrate how such designs can be implemented through sample splitting. Empirically, we demonstrate that two-stage designs improve upon single-stage approaches, especially for scenarios where domain knowledge is available through a prior. Our work is thus, a simple yet effective design for RCTs, optimizing for the ability to certify with high probability the largest possible treatment effect for at least one of the arms studied.

Estimation and inference for the Average Treatment Effect (ATE) is a cornerstone of causal inference and often serves as the foundation for developing procedures for more complicated settings. Although traditionally analyzed in a batch setting, recent advances in martingale theory have paved the way for adaptive methods that can enhance the power of downstream inference. Despite these advances, progress in understanding and developing adaptive algorithms remains in its early stages. Existing work either focus on asymptotic analyses that overlook exploration-exploitation trade-offs relevant in finite-sample regimes or rely on simpler but suboptimal estimators. In this work, we address these limitations by studying adaptive sampling procedures that take advantage of the asymptotically optimal Augmented Inverse Probability Weighting (AIPW) estimator. Our analysis uncovers challenges obscured by asymptotic approaches and introduces a novel algorithmic design principle reminiscent of optimism in multi-armed bandits. This principled approach enables our algorithm to achieve significant theoretical and empirical gains compared to previous methods. Our findings mark a step forward in the advancement of adaptive causal inference methods in theory and practice.

Reinforcement Learning with Human Feedback (RLHF) is a widely used fine-tuning approach that aligns machine learning models, particularly Language Models (LMs) with human preferences. There are typically multiple objectives driving the preference, hence humans find it easier to express per-objective comparisons rather than a global preference between two choices, e.g. compare two papers on their novelty, clarity, correctness, etc. Multi-Objective RLHF aims to use per-objective preference feedback and achieve a Pareto optimal tradeoff among these objectives by aggregating them into a single unified objective for optimization. However, nearly all prior works rely on linear aggregation, which rules out policies that favor specific objectives such as the worst one. The only existing approach using non-linear aggregation is computationally expensive due to its reward-based nature and the need for retraining whenever the aggregation parameters change. In this work, we address this limitation by transforming the non-linear aggregation maximization problem into a series of sub-problems. Each sub-problem involves only linear aggregation, making it computationally efficient to solve. We further extend our framework to handle multi-group scenarios, where each group has distinct weights for the objectives. Our method enables achieving consensus or maximizing the aggregated objective across all groups. Theoretically, we demonstrate that our algorithmic framework achieves sublinear regret and can be easily adapted to a reward-free algorithm. Empirically, leveraging our theoretical insights, we propose a nearly training-free algorithm once the optimal policies for individual objectives are obtained.

The ability to reason lies at the core of artificial intelligence (AI), and challenging problems usually call for deeper and longer reasoning to tackle. A crucial question about AI reasoning is whether models can extrapolate learned reasoning patterns to solve harder tasks with a longer chain-of-thought (CoT). In this work, we present a theoretical analysis of transformers learning on synthetic state-tracking tasks with gradient descent. Specifically: 1). We prove how the *algebraic structure* of state-tracking problems governs the length generalization of learned reasoning in transformers. In doing so, we formulate the **attention concentration** mechanism, linking the retrieval robustness of the attention layer to the task structure of long-context state tracking problems. 2). Moreover, we prove that a transformer can provably *self-improve* via a *recursive self-training* scheme that progressively extends the range of solvable problem lengths. We show that the model can achieve abilities outside the coverage of the base model in recursive training, different from prior theoretical works on self-improvement. To our knowledge, we provide the first *optimization guarantee* that constant-depth transformers provably learn $\text{NC}^1$-complete problems with CoT, significantly going beyond prior art confined in $\text{TC}^0$, unless the widely held conjecture $\text{TC}^0 \neq \text{NC}^1$ fails. Finally, we present a broad set of experiments supporting our theoretical results, confirming the length generalization behaviors and the mechanism of attention concentration.

Partial observability is a notorious challenge in reinforcement learning (RL), due to the need to learn complex, history-dependent policies. Recent empirical successes have used *privileged expert distillation* -- which leverages availability of latent state information during training (e.g., from a simulator) to learn and imitate the optimal latent, Markovian policy -- to disentangle the task of ''learning to see'' from ''learning to act''. While expert distillation is more computationally efficient than RL without latent state information, it also has well-documented failure modes. In this paper -- through a simple but instructive theoretical model called the *perturbed Block MDP*, and controlled experiments on challenging simulated locomotion tasks -- we investigate the algorithmic trade-off between privileged expert distillation and standard RL without privileged information. Our main findings are: **(1)** The trade-off empirically hinges on the *stochasticity* of the latent dynamics, as theoretically predicted by contrasting *approximate decodability* with *belief contraction* in the perturbed Block MDP; and **(2)** The optimal latent policy is not always the best latent policy to distill. Our results suggest new guidelines for effectively exploiting privileged information, potentially advancing the efficiency of policy learning across many practical partially observable domains.

Vision tasks are characterized by the properties of locality and translation invariance. The superior performance of convolutional neural networks (CNNs) on these tasks is widely attributed to the inductive bias of locality and weight sharing baked into their architecture. Existing attempts to quantify the statistical benefits of these biases in CNNs over locally connected convolutional neural networks (LCNs) and fully connected neural networks (FCNs) fall into one of the following categories: either they disregard the optimizer and only provide uniform convergence upper bounds with no separating lower bounds, or they consider simplistic tasks that do not truly mirror the locality and translation invariance as found in real-world vision tasks. To address these deficiencies, we introduce the Dynamic Signal Distribution (DSD) classification task that models an image as consisting of $k$ patches, each of dimension $d$, and the label is determined by a $d$-sparse signal vector that can freely appear in any one of the $k$ patches. On this task, for any orthogonally equivariant algorithm like gradient descent, we prove that CNNs require $\tilde{O}(k+d)$ samples, whereas LCNs require $\Omega(kd)$ samples, establishing the statistical advantages of weight sharing in translation invariant tasks. Furthermore, LCNs need $\tilde{O}(k(k+d))$ samples, compared to $\Omega(k^2d)$ samples for FCNs, showcasing the benefits of locality in local tasks. Additionally, we develop information theoretic tools for analyzing randomized algorithms, which may be of interest for statistical research.

We consider the hybrid reinforcement learning setting where the agent has access to both offline data and online interactive access. While RL research typically assumes offline data contains complete action, reward and transition information, datasets with only state information (also known as observation-only datasets) are more general, abundant and practical. This motivates our study of the hybrid RL with observation-only offline dataset framework. While the task of competing with the best policy “covered” by the offline data can be solved if a reset model of the environment is provided (i.e., one that can be reset to any state), we show evidence of hardness of competing when only given the weaker trace model (i.e., one can only reset to the initial states and must produce full traces through the environment), without further assumption of admissibility of the offline data. Under the admissibility assumptions– that the offline data could actually be produced by the policy class we consider– we propose the first algorithm in the trace model setting that provably matches the performance of algorithms that leverage a reset model. We also perform proof-of-concept experiments that suggest the effectiveness of our algorithm in practice.

Learning from human preference data has emerged as the dominant paradigm for fine-tuning large language models (LLMs). The two most common families of techniques -- online reinforcement learning (RL) such as Proximal Policy Optimization (PPO) and offline contrastive methods such as Direct Preference Optimization (DPO) -- were positioned as equivalent in prior work due to the fact that both have to start from the same offline preference dataset. To further expand our theoretical understanding of the similarities and differences between online and offline techniques for preference fine-tuning, we conduct a rigorous analysis through the lens of *dataset coverage*, a concept that captures how the training data covers the test distribution and is widely used in RL. We prove that a global coverage condition is both necessary and sufficient for offline contrastive methods to converge to the optimal policy, but a weaker partial coverage condition suffices for online RL methods. This separation provides one explanation of why online RL methods can perform better than offline methods, especially when the offline preference data is not diverse enough. Finally, motivated by our preceding theoretical observations, we derive a hybrid preference optimization (HyPO) algorithm that uses offline data for contrastive-based preference optimization and online unlabeled data for KL regularization. Theoretically and empirically, we demonstrate that HyPO is more performant than its pure offline counterpart DPO, while still preserving its computation and memory efficiency.

Is it possible to understand or imitate a policy maker's rationale by looking at past decisions they made? We formalize this question as the problem of learning social welfare functions belonging to the well-studied family of power mean functions. We focus on two learning tasks; in the first, the input is vectors of utilities of an action (decision or policy) for individuals in a group and their associated social welfare as judged by a policy maker, whereas in the second, the input is pairwise comparisons between the welfares associated with a given pair of utility vectors. We show that power mean functions are learnable with polynomial sample complexity in both cases, even if the social welfare information is noisy. Finally, we design practical algorithms for these tasks and evaluate their performance.

Radar collision prediction systems can play a crucial role in safety critical applications, such as autonomous vehicles and smart helmets for contact sports, by predicting an impending collision just before it will occur. Collision prediction algorithms use the velocity and range measurements provided by radar to calculate time to collision. However, radar measurements used in such systems contain significant clutter, noise, and inaccuracies which hamper reliability. Existing solutions to reduce clutter are based on static filtering methods. In this paper, we present a deep learning approach using frequency modulated continuous wave (FMCW) radar and inertial sensing that learns the environmental and user-specific conditions that lead to future collisions. We present a process of converting raw radar samples to range-Doppler matrices (RDMs) and then training a deep convolutional neural network that outputs predictions (impending collision vs. none) for any measured RDM. The system is retrained to work in dynamically changing environments and maintain prediction accuracy. We demonstrate the effectiveness of our approach of using the information from radar data to predict impending collisions in real-time via real-world experiments, and show that our method achieves an F1-score of 0.91 and outperforms a traditional approach in accuracy and adaptability.

In continuum-armed bandit problems where the underlying function resides in a reproducing kernel Hilbert space (RKHS), namely, the kernelised bandit problems, an important open problem remains of how well learning algorithms can adapt if the regularity of the associated kernel function is unknown. In this work, we study adaptivity to the regularity of translation-invariant kernels, which is characterized by the decay rate of the Fourier transformation of the kernel, in the bandit setting. We derive an adaptivity lower bound, proving that it is impossible to simultaneously achieve optimal cumulative regret in a pair of RKHSs with different regularities. To verify the tightness of this lower bound, we show that an existing bandit model selection algorithm applied with minimax non-adaptive kernelised bandit algorithms matches the lower bound in dependence of T, the total number of steps, except for log factors. By filling in the regret bounds for adaptivity between RKHSs, we connect the statistical difficulty for adaptivity in continuum-armed bandits in three fundamental types of function spaces: RKHS, Sobolev space, and Holder space.

In human-interactive applications of online learning, a human's preferences or abilities are often a function of the algorithm's recent actions. Motivated by this, a significant line of work has formalized settings where an action's loss is a function of the number of times it was played in the prior $m$ timesteps, where $m$ corresponds to a bound on human memory capacity. To more faithfully capture decay of human memory with time, we introduce the Weighted Tallying Bandit (WTB), which generalizes this setting by requiring that an action's loss is a function of a *weighted* summation of the number of times it was played in the last $m$ timesteps. WTB is intractable without further assumption. So we study it under Repeated Exposure Optimality (REO), a condition requiring the existence of an action that when repetitively played will eventually yield smaller loss than any other action sequence. We study the minimization of complete policy regret (CPR), which is the strongest notion of regret, in WTB under REO. Since $m$ is often unknown, we only assume access to an upper bound $M$ on $m$. We show that for problems with $K$ actions and horizon $T$, a simple modification of the successive elimination algorithm has $\mathcal{O} \left( \sqrt{KT} + (m+M)K \right)$ CPR. Upto an additive (in lieu of mutliplicative) factor in $(m+M)K$, this recovers the classical guarantee for the far simpler stochastic multi-armed bandit with traditional regret. We additionally show that in our setting, any algorithm will suffer additive CPR of $\Omega \left( mK + M \right)$, demonstrating our result is near optimal. Our method is computationally efficient, and we experimentally demonstrate its practicality and superiority over various baselines.

We propose a novel approach to addressing two fundamental challenges in Model-based Reinforcement Learning (MBRL): the computational expense of repeatedly finding a good policy in the learned model, and the objective mismatch between model fitting and policy computation. Our "lazy" method leverages a novel unified objective, Performance Difference via Advantage in Model, to capture the performance difference between the learned policy and expert policy under the true dynamics. This objective demonstrates that optimizing the expected policy advantage in the learned model under an exploration distribution is sufficient for policy computation, resulting in a significant boost in computational efficiency compared to traditional planning methods. Additionally, the unified objective uses a value moment matching term for model fitting, which is aligned with the model’s usage during policy computation. We present two no-regret algorithms to optimize the proposed objective, and demonstrate their statistical and computational gains compared to existing MBRL methods through simulated benchmarks.

Software defined radios (SDRs) are often used in the experimental evaluation of next-generation wireless technologies. While crowdsourced spectrum monitoring is an important component of future spectrum-agile technologies, there is no clear way to test it in the real world, i.e., with hundreds of users each carrying an SDR while uploading data to a cloud-based controller. Current fully functional SDRs are bulky, with components connected via wires, and last at most hours on a single battery charge. To address these needs, we design and develop a compact, portable, untethered, and inexpensive SDR we callSitara. Our SDR interfaces with a mobile device over Bluetooth 5 and can function standalone or as a client to a central command and control server. It transmits and receives common waveforms, uploads IQ samples or processed receiver data through a mobile device to a server for remote processing and performs spectrum sensing functions. We present results from a user study involving more than 100 participants to evaluate Sitara in a hypothetical large-scale crowdsourced spectrum monitoring application. We also present a comparative analysis of Sitara to related crowdsensing systems with a particular emphasis on the role of incentives and user participation.

Policy regret is a well established notion of measuring the performance of an online learning algorithm against an adaptive adversary. We study restrictions on the adversary that enable efficient minimization of the \emph{complete policy regret}, which is the strongest possible version of policy regret. We identify a gap in the current theoretical understanding of what sorts of restrictions permit tractability in this challenging setting. To resolve this gap, we consider a generalization of the stochastic multi armed bandit, which we call the \emph{tallying bandit}. This is an online learning setting with an $m$-memory bounded adversary, where the average loss for playing an action is an unknown function of the number (or tally) of times that the action was played in the last $m$ timesteps. For tallying bandit problems with $\numact$ actions and time horizon $T$, we provide an algorithm that w.h.p achieves a complete policy regret guarantee of $\bigo ( m \numact \sqrt{T} )$, where the $\bigo$ notation hides only logarithmic factors. We additionally prove an $\bigomega(\sqrt{ m \numact T})$ lower bound on the expected complete policy regret of any tallying bandit algorithm, demonstrating the near optimality of our method.

A number of applications require two-sample testing on ranked preference data. For instance, in crowdsourcing, there is a long-standing question of whether pairwise-comparison data provided by people is distributed identically to ratings-converted-to-comparisons. Other applications include sports data analysis and peer grading. In this paper, we design twosample tests for pairwise-comparison data and ranking data. For our two-sample test for pairwise-comparison data, we establish an upper bound on the sample complexity required to correctly test whether the distributions of the two sets of samples are identical. Our test requires essentially no assumptions on the distributions. We then prove complementary lower bounds showing that our results are tight (in the minimax sense) up to constant factors. We investigate the role of modeling assumptions by proving lower bounds for a range of pairwise-comparison models (WST, MST, SST, parameter-based such as BTL and Thurstone). We also provide tests and associated sample complexity bounds for partial (or total) ranking data. Furthermore, we empirically evaluate our results via extensive simulations as well as three real-world data sets consisting of pairwise-comparisons and rankings. By applying our two-sample test on real-world pairwise-comparison data, we conclude that ratings and rankings provided by people are indeed distributed differently.

We consider the issue of strategic behaviour in various peer-assessment tasks, including peer grading of exams or homeworks and peer review in hiring or promotions. When a peer-assessment task is competitive (e.g., when students are graded on a curve), agents may be incentivized to misreport evaluations in order to improve their own final standing. Our focus is on designing methods for detection of such manipulations. Specifically, we consider a setting in which agents evaluate a subset of their peers and output rankings that are later aggregated to form a final ordering. In this paper, we investigate a statistical framework for this problem and design a principled test for detecting strategic behaviour. We prove that our test has strong false alarm guarantees and evaluate its detection ability in practical settings. For this, we design and conduct an experiment that elicits strategic behaviour from subjects and release a dataset of patterns of strategic behaviour that may be of independent interest. We use this data to run a series of real and semi-synthetic evaluations that reveal a strong detection power of our test.

Conference peer review constitutes a human-computation process whose importance cannot be overstated: not only it identifies the best submissions for acceptance, but, ultimately, it impacts the future of the whole research area by promoting some ideas and restraining others. A surge in the number of submissions received by leading AI conferences has challenged the sustainability of the review process by increasing the burden on the pool of qualified reviewers which is growing at a much slower rate. In this work, we consider the problem of reviewer recruiting with a focus on the scarcity of qualified reviewers in large conferences. Specifically, we design a procedure for (i) recruiting reviewers from the population not typically covered by major conferences and (ii) guiding them through the reviewing pipeline. In conjunction with the ICML 2020 --- a large, top-tier machine learning conference --- we recruit a small set of reviewers through our procedure and compare their performance with the general population of ICML reviewers. Our experiment reveals that a combination of the recruiting and guiding mechanisms allows for a principled enhancement of the reviewer pool and results in reviews of superior quality compared to the conventional pool of reviews as evaluated by senior members of the program committee (meta-reviewers).

We consider bandit optimization of a smooth reward function, where the goal is cumulative regret minimization. This problem has been studied for $\alpha$-Holder continuous (including Lipschitz) functions with $0<\alpha\leq 1$. Our main result is in generalization of the reward function to Holder space with exponent $\alpha>1$ to bridge the gap between Lipschitz bandits and infinitely-differentiable models such as linear bandits. For Holder continuous functions, approaches based on random sampling in bins of a discretized domain suffices as optimal. In contrast, we propose a class of two-layer algorithms that deploy misspecified linear/polynomial bandit algorithms in bins. We demonstrate that the proposed algorithm can exploit higher-order smoothness of the function by deriving a regret upper bound of $\tilde{O}(T^\frac{d+\alpha}{d+2\alpha})$ for when $\alpha>1$, which matches existing lower bound. We also study adaptation to unknown function smoothness over a continuous scale of Holder spaces indexed by $\alpha$, with a bandit model selection approach applied with our proposed two-layer algorithms. We show that it achieves regret rate that matches the existing lower bound for adaptation within the $\alpha\leq 1$ subset.

Real-time proximity and collision detection via radio distance measurements has application in smart-helmets, drones, autonomous vehicles, and social distancing. In this paper we present a range-based, infrastructure-free, distributed algorithm that utilizes inter-robot range data and intra-robot acceleration data to estimate each robot's recent positions. As the next step, a collision prediction scheme is proposed that uses the derived relative kinematics of each robot to predict an impending collision between any pair of robot. The algorithm is tested and validated with the help of measurement trace-based simulation of motion involving acceleration.

Neural networks have been shown to outperform kernel methods in practice (including neural tangent kernels). Most theoretical explanations of this performance gap focus on learning a complex hypothesis class; in some cases, it is unclear whether this hypothesis class captures realistic data. In this work, we propose a related, but alternative, explanation for this performance gap in the image classification setting, based on finding a sparse signal in the presence of noise. Specifically, we prove that, for a simple data distribution with sparse signal amidst high-variance noise, a simple convolutional neural network trained using stochastic gradient descent learns to threshold out the noise and find the signal. On the other hand, the corresponding neural tangent kernel, with a fixed set of predetermined features, is unable to adapt to the signal in this manner. We supplement our theoretical results by demonstrating this phenomenon empirically: in CIFAR-10 and MNIST images with various backgrounds, as the background noise increases in intensity, a CNN's performance stays relatively robust, whereas its corresponding neural tangent kernel sees a notable drop in performance. We therefore propose the "local signal adaptivity" (LSA) phenomenon as one explanation for the superiority of neural networks over kernel methods.

We consider the problem of automated assignment of papers to reviewers in conference peer review, with a focus on fairness and statistical accuracy. Our fairness objective is to maximize the review quality of the most disadvantaged paper, in contrast to the commonly used objective of maximizing the total quality over all papers. We design an assignment algorithm based on an incremental max-flow procedure that we prove is near-optimally fair. Our statistical accuracy objective is to ensure correct recovery of the papers that should be accepted. We provide a sharp minimax analysis of the accuracy of the peer-review process for a popular objective-score model as well as for a novel subjective-score model that we propose in the paper. Our analysis proves that our proposed assignment algorithm also leads to a near-optimal statistical accuracy. Finally, we design a novel experiment that allows for an objective comparison of various assignment algorithms, and overcomes the inherent difficulty posed by the absence of a ground truth in experiments on peer-review. The results of this experiment as well as of other experiments on synthetic and real data corroborate the theoretical guarantees of our algorithm.

Modern machine learning and computer science conferences are experiencing a surge in the number of submissions that challenges the quality of peer review as the number of competent reviewers is growing at a much slower rate. To curb this trend and reduce the burden on reviewers, several conferences have started encouraging or even requiring authors to declare the previous submission history of their papers. Such initiatives have been met with skepticism among authors, who raise the concern about a potential bias in reviewers' recommendations induced by this information. In this work, we investigate whether reviewers exhibit a bias caused by the knowledge that the submission under review was previously rejected at a similar venue, focusing on a population of novice reviewers who constitute a large fraction of the reviewer pool in leading machine learning and computer science conferences. We design and conduct a randomized controlled trial closely replicating the relevant components of the peer-review pipeline with $133$ reviewers (master's, junior PhD students, and recent graduates of top US universities) writing reviews for $19$ papers. The analysis reveals that reviewers indeed become negatively biased when they receive a signal about paper being a resubmission, giving almost 1 point lower overall score on a 10-point Likert item (Δ = -0.78, 95% CI = [-1.30, -0.24]) than reviewers who do not receive such a signal. Looking at specific criteria scores (originality, quality, clarity and significance), we observe that novice reviewers tend to underrate quality the most.

The Thresholding Bandit Problem (TBP) aims to find the set of arms with mean rewards greater than a given threshold. We consider a new setting of TBP, where in addition to pulling arms, one can also duel two arms and get the arm with a greater mean. In our motivating application from crowdsourcing, dueling two arms can be more cost-effective and time-efficient than direct pulls. We refer to this problem as TBP with Dueling Choices (TBP-DC). This paper provides an algorithm called Rank-Search (RS) for solving TBP-DC by alternating between ranking and binary search. We prove theoretical guarantees for RS, and also give lower bounds to show the optimality of it. Experiments show that RS outperforms previous baseline algorithms that only use pulls or duels.

A number of applications require two-sample testing of pairwise comparison data. For instance, in crowdsourcing, there is a long-standing question of whether comparison data provided by people is distributed similar to ratings-converted-to-comparisons. Other examples include sports data analysis and peer grading. In this paper, we design a two-sample test for pairwise comparison data. We establish an upper bound on the sample complexity required to correctly distinguish between the distributions of the two sets of samples. Our test requires essentially no assumptions on the distributions. We then prove complementary information-theoretic lower bounds showing that our results are tight (in the minimax sense) up to constant factors. We also investigate the role of modeling assumptions by proving information-theoretic lower bounds for a range of pairwise comparison models (WST, MST, SST, parameter-based such as BTL and Thurstone).

Preference-based Reinforcement Learning (PbRL) replaces reward values in traditional reinforcement learning by preferences to better elicit human opinion on the target objective, especially when numerical reward values are hard to design or interpret. Despite promising results in applications, the theoretical understanding of PbRL is still in its infancy. In this paper, we present the first finite-time analysis for general PbRL problems. We first show that a unique optimal policy may not exist if preferences over trajectories are deterministic for PbRL. If preferences are stochastic, and the preference probability relates to the hidden reward values, we present algorithms for PbRL, both with and without a simulator, that are able to identify the best policy up to accuracy $\varepsilon$ with high probability. Our method explores the state space by navigating to under-explored states, and solves PbRL using a combination of dueling bandits and policy search. Experiments show the efficacy of our method when it is applied to real-world problems.

We consider a novel setting of zeroth order non-convex optimization, where in addition to querying the function value at a given point, we can also duel two points and get the point with the larger function value. We refer to this setting as optimization with dueling-choice bandits, since both direct queries and duels are available for optimization. We give the COMP-GP-UCB algorithm based on GP-UCB (Srinivas et al., 2009),, where instead of directly querying the point with the maximum Upper Confidence Bound (UCB), we perform constrained optimization and use comparisons to filter out suboptimal points. COMP-GP-UCB comes with theoretical guarantee of $O(\frac{\Phi}{\sqrt{T}})$ on simple regret where $T$ is the number of direct queries and $\Phi$ is an improved information gain stemming from a comparison-based constraint set that restricts the space for optimum search. In contrast, in the plain direct query setting, $\Phi$ depends on the entire domain. We discuss theoretical aspects and show experimental results to demonstrate efficacy of our algorithm.

In supervised learning, we typically leverage a fully labeled dataset to design methods for function estimation or prediction. In many practical situations, we are able to obtain alternative feedback, possibly at a low cost. A broad goal is to understand the usefulness of, and to design algorithms to exploit, this alternative feedback. In this paper, we consider a semi-supervised regression setting, where we obtain additional ordinal (or comparison) information for the unlabeled samples. We consider ordinal feedback of varying qualities where we have either a perfect ordering of the samples, a noisy ordering of the samples or noisy pairwise comparisons between the samples. We provide a precise quantification of the usefulness of these types of ordinal feedback in both nonparametric and linear regression, showing that in many cases it is possible to accurately estimate an underlying function with a very small labeled set, effectively escaping the curse of dimensionality. We also present lower bounds, that establish fundamental limits for the task and show that our algorithms are optimal in a variety of settings. Finally, we present extensive experiments on new datasets that demonstrate the efficacy and practicality of our algorithms and investigate their robustness to various sources of noise and model misspecification.

A major challenge in understanding the generalization of deep learning is to explain why (stochastic) gradient descent can exploit the network architecture to find solutions that have good generalization performance when using high capacity models. We find simple but realistic examples showing that this phenomenon exists even when learning linear classifiers — between two linear networks with the same capacity, the one with a convolutional layer can generalize better than the other when the data distribution has some underlying spatial structure. We argue that this difference results from a combination of the convolution architecture, data distribution and gradient descent, all of which are necessary to be included in a meaningful analysis. We analyze of the generalization performance as a function of data distribution and convolutional filter size, given gradient descent as the optimization algorithm, then interpret the results using concrete examples. Experimental results show that our analysis is able to explain what happens in our introduced examples.

We consider the problem of automated assignment of papers to reviewers in conference peer review, with a focus on fairness and statistical accuracy. Our fairness objective is to maximize the review quality of the most disadvantaged paper, in contrast to the popular objective of maximizing the total quality over all papers. We design an assignment algorithm based on an incremental max-flow procedure that we prove is near-optimally fair. Our statistical accuracy objective is to ensure correct recovery of the papers that should be accepted. With a sharp minimax analysis we also prove that our algorithm leads to assignments with strong statistical guarantees both in an objective-score model as well as a novel subjective-score model that we propose in this paper.

We consider the issue of biases in scholarly research, specifically, in peer review. There is a long standing debate on whether exposing author identities to reviewers induces biases against certain groups, and our focus is on designing tests to detect the presence of such biases. Our starting point is a remarkable recent work by Tomkins, Zhang and Heavlin which conducted a controlled, large-scale experiment to investigate existence of biases in the peer reviewing of the WSDM conference. We present two sets of results in this paper. The first set of results is negative, and pertains to the statistical tests and the experimental setup used in the work of Tomkins et al. We show that the test employed therein does not guarantee control over false alarm probability and under correlations between relevant variables, coupled with any of the following conditions, with high probability can declare a presence of bias when it is in fact absent: (a) measurement error, (b) model mismatch, (c) reviewer calibration. Moreover, we show that the setup of their experiment may itself inflate false alarm probability if (d) bidding is performed in non-blind manner or (e) popular reviewer assignment procedure is employed. Our second set of results is positive, in that we present a general framework for testing for biases in (single vs. double blind) peer review. We then present a hypothesis test with guaranteed control over false alarm probability and non-trivial power even under conditions (a)--(c). Conditions (d) and (e) are more fundamental problems that are tied to the experimental setup and not necessarily related to the test.

We consider the problem of global optimization of an unknown non-convex smooth function with noisy zeroth-order feedback. We propose a local minimax framework to study the fundamental difficulty of optimizing smooth functions with adaptive function evaluations. We show that for functions with fast growth around their global minima, carefully designed optimization algorithms can identify a near global minimizer with many fewer queries than worst-case global minimax theory predicts. For the special case of strongly convex and smooth functions, our implied convergence rates match the ones developed for zeroth-order convex optimization problems. On the other hand, we show that in the worst case no algorithm can converge faster than the minimax rate of estimating an unknown function in the ℓ∞-norm. Finally, we show that non-adaptive algorithms, though optimal in a global minimax sense, do not attain the optimal local minimax rate.

Subspace clustering is the problem of partitioning unlabeled data points into a number of clusters so that data points within one cluster lie approximately on a low-dimensional linear subspace. In many practical scenarios, the dimensionality of data points to be clustered is compressed due to the constraints of measurement, computation, or privacy. In this paper, we study the theoretical properties of a popular subspace clustering algorithm named sparse subspace clustering (SSC) and establish formal success conditions of SSC on dimensionality-reduced data. Our analysis applies to the most general fully deterministic model, where both underlying subspaces and data points within each subspace are deterministically positioned, and also a wide range of dimensionality reduction techniques (e.g., Gaussian random projection, uniform subsampling, and sketching) that fall into a subspace embedding framework. Finally, we apply our analysis to a differentially private SSC algorithm and established both privacy and utility guarantees of the proposed method.

We consider the problem of optimizing a high-dimensional convex function using stochastic zeroth-order queries. Under sparsity assumptions on the gradients or function values, we present two algorithms: a successive component/feature selection algorithm and a noisy mirror descent algorithm using Lasso gradient estimates, and show that both algorithms have convergence rates that depend only logarithmically on the ambient dimension of the problem. Empirical results confirm our theoretical findings and show that the algorithms we design outperform classical zeroth-order optimization methods in the high-dimensional setting.

In this paper we consider the problem of allocation of measurement bits in order to reduce the statistical signal recovery error resulting from quantization error. We propose a continuous optimization problem that serves as a relaxation of the original combinatorial problem, which is amenable to classical continuous optimization solvers such as the gradient descent. We also design a “rounding” algorithm based on the idea of effective resistance sampling to turn the continuous fractional solution into a feasible bit allocation strategy with integer number of bits allocated to each design point.

We consider the problem of learning an one-hidden-layer neural network with non-overlapping convolutional layer and ReLU activation function, i.e., $f(Z; w, a) = \sum_j a_j\sigma(w^\top Z_j)$, in which both the convolutional weights $w$ and the output weights $a$ are parameters to be learned. We prove that with Gaussian input $\mathbf{Z}$ there is a spurious local minimizer. Surprisingly, in the presence of the spurious local minimizer, starting from randomly initialized weights, gradient descent with weight normalization can still be proven to recover the true parameters with constant probability (which can be boosted to probability $1$ with multiple restarts). We also show that with constant probability, the same procedure could also converge to the spurious local minimum, showing that the local minimum plays a non-trivial role in the dynamics of gradient descent. Furthermore, a quantitative analysis shows that the gradient descent dynamics has two phases: it starts off slow, but converges much faster after several iterations.

In supervised learning, we leverage a labeled dataset to design methods for function estimation. In many practical situations, we are able to obtain alternative feedback, possibly at a low cost. A broad goal is to understand the usefulness of, and to design algorithms to exploit, this alternative feedback. We focus on a semi-supervised setting where we obtain additional ordinal (or comparison) information for potentially unlabeled samples. We consider ordinal feedback of varying qualities where we have either a perfect ordering of the samples, a noisy ordering of the samples or noisy pairwise comparisons between the samples. We provide a precise quantification of the usefulness of these types of ordinal feedback in non-parametric regression, showing that in many cases it is possible to accurately estimate an underlying function with a very small labeled set, effectively escaping the curse of dimensionality. We develop an algorithm called Ranking-Regression (RR) and analyze its accuracy as a function of size of the labeled and unlabeled datasets and various noise parameters. We also present lower bounds, that establish fundamental limits for the task and show that RR is optimal in a variety of settings. Finally, we present experiments that show the efficacy of RR and investigate its robustness to various sources of noise and model-misspecification.

A widespread folklore for explaining the success of Convolutional Neural Networks (CNNs) is that CNNs use a more compact representation than the Fully-connected Neural Network (FNN) and thus require fewer training samples to accurately estimate their parameters. We initiate the study of rigorously characterizing the sample complexity of estimating CNNs. We show that for an $m$-dimensional convolutional filter with linear activation acting on a $d$-dimensional input, the sample complexity of achieving population prediction error of $\epsilon$ is $\widetilde{O(m/\epsilon^2)$, whereas the sample-complexity for its FNN counterpart is lower bounded by $\Omega(d/\epsilon^2)$ samples. Since, in typical settings $m \ll d$, this result demonstrates the advantage of using a CNN. We further consider the sample complexity of estimating a one-hidden-layer CNN with linear activation where both the $m$-dimensional convolutional filter and the $r$-dimensional output weights are unknown. For this model, we show that the sample complexity is $\widetilde{O}\left((m+r)/\epsilon^2\right)$ when the ratio between the stride size and the filter size is a constant. For both models, we also present lower bounds showing our sample complexities are tight up to logarithmic factors. Our main tools for deriving these results are a localized empirical process analysis and a new lemma characterizing the convolutional structure. We believe that these tools may inspire further developments in understanding CNNs.

We consider the problem of global optimization of an unknown non-convex smooth function with noisy zeroth-order feedback. We propose a local minimax framework to study the fundamental difficulty of optimizing smooth functions with adaptive function evaluations. We show that for functions with fast growth around their global minima, carefully designed optimization algorithms can identify a near global minimizer with many fewer queries than worst-case global minimax theory predicts. For the special case of strongly convex and smooth functions, our implied convergence rates match the ones developed for zeroth-order convex optimization problems. On the other hand, we show that in the worst case no algorithm can converge faster than the minimax rate of estimating an unknown functions in linf-norm. Finally, we show that non-adaptive algorithms, although optimal in a global minimax sense, do not attain the optimal local minimax rate.

Large bundles of myelinated axons, called white matter, anatomically connect disparate brain regions together and compose the structural core of the human connectome. We recently proposed a method of measuring the local integrity along the length of each white matter fascicle, termed the local connectome [1]. If communication efficiency is fundamentally constrained by the integrity along the entire length of a white matter bundle [2], then variability in the functional dynamics of brain networks should be associated with variability in the local connectome. We test this prediction using two statistical approaches that are capable of handling the high dimensionality of data. First, by performing statistical inference on distance-based correlations, we show that similarity in the local connectome between individuals is significantly correlated with similarity in their patterns of functional connectivity. Second, by employing variable selection using sparse canonical correlation analysis and cross-validation, we show that segments of the local connectome are predictive of certain patterns of functional brain dynamics. These results are consistent with the hypothesis that structural variability along axon bundles constrains communication between disparate brain regions.

This paper studies the problem of estimating the covariance of a collection of vectors using only highly compressed measurements of each vector. An estimator based on back-projections of these compressive samples is proposed and analyzed. A distribution-free analysis shows that by observing just a single linear measurement of each vector, one can consistently estimate the covariance matrix, in both infinity and spectral norm, and this analysis leads to precise rates of convergence in both norms. Through information-theoretic techniques, lower bounds showing that this estimator is minimax-optimal for both infinity and spectral norm estimation problems are established. These results are also specialized to give matching upper and lower bounds for estimating the population covariance of a collection of Gaussian vectors, again in the compressive measurement model. The analysis conducted in this paper shows that the effective sample complexity for this problem is scaled by a factor of m2/d2, where m is the compression dimension and d is the ambient dimension. Applications to subspace learning (principal components analysis) and learning over distributed sensor networks are also discussed.

Many conventional statistical procedures are extremely sensitive to seemingly minor deviations from modeling assumptions. This problem is exacerbated in modern high-dimensional settings, where the problem dimension can grow with and possibly exceed the sample size. We consider the problem of robust estimation of sparse functionals, and provide a computationally and statistically efficient algorithm in the high-dimensional setting. Our theory identifies a unified set of deterministic conditions under which our algorithm guarantees accurate recovery. By further establishing that these deterministic conditions hold with high-probability for a wide range of statistical models, our theory applies to many problems of considerable interest including sparse mean and covariance estimation; sparse linear regression; and sparse generalized linear models. In certain settings, such as the detection and estimation of sparse principal components in the spiked covariance model, our general theory does not yield optimal sample complexity, and we provide a novel algorithm based on the same intuition which is able to take advantage of further structure of the problem to achieve nearly optimal rates.

We consider computationally tractable methods for the experimental design problem, where k out of n design points of dimension p are selected so that certain optimality criteria are approximately satisfied. Our algorithm finds a $(1+\epsilon)$-approximate optimal design when k is a linear function of p; in contrast, existing results require k to be super-linear in p. Our algorithm also handles all popular optimality criteria, while existing ones only handle one or two such criteria. Numerical results on synthetic and real-world design problems verify the practical effectiveness of the proposed algorithm.

Latent space models (LSMs) provide a principled and effective way to extract hidden patterns from observed data. To cope with two challenges in LSMs: (1) how to capture infrequent patterns when pattern frequency is imbalanced and (2) how to reduce model size without sacrificing their expressiveness, several studies have been proposed to “diversify” LSMs, which design regularizers to encourage the components therein to be “diverse”. In light of the limitations of existing approaches, we design a new diversity-promoting regularizer by considering two factors: uncorrelation and evenness, which encourage the components to be uncorrelated and to play equally important roles in modeling data. Formally, this amounts to encouraging the covariance matrix of the components to have more uniform eigenvalues. We apply the regularizer to two LSMs and develop an efficient optimization algorithm. Experiments on healthcare, image and text data demonstrate the effectiveness of the regularizer.

Although gradient descent (GD) almost always escapes saddle points asymptotically [Lee et al., 2016], this paper shows that even with fairly natural random initialization schemes and non-pathological functions, GD can be significantly slowed down by saddle points, taking exponential time to escape. On the other hand, gradient descent with perturbations [Ge et al., 2015, Jin et al., 2017] is not slowed down by saddle points—it can find an approximate local minimizer in polynomial time. This result implies that GD is inherently slower than perturbed GD, and justifies the importance of adding perturbations for efficient non-convex optimization. While our focus is theoretical, we also present experiments that illustrate our theoretical findings.

We consider the Hypothesis Transfer Learning (HTL) problem where one incorporates a hypothesis trained on the source domain into the learning procedure of the target domain. Existing theoretical analysis either only studies specific algorithms or only presents upper bounds on the generalization error but not on the excess risk. In this paper, we propose a unified algorithm-dependent framework for HTL through a novel notion of transformation functions, which characterizes the relation between the source and the target domains. We conduct a general risk analysis of this framework and in particular, we show for the first time, if two domains are related, HTL enjoys faster convergence rates of excess risks for Kernel Smoothing and Kernel Ridge Regression than those of the classical non-transfer learning settings. We accompany this framework with an analysis of cross-validation for HTL to search for the best transfer technique and gracefully reduce to non-transfer learning when HTL is not helpful. Experiments on robotics and neural imaging data demonstrate the effectiveness of our framework.

We show that given an estimate $\widehat{\mat A}$ that is close to a general high-rank positive semi-definite (PSD) matrix $\mat A$ in spectral norm (i.e., $\|\widehat{\mat A}-\mat A\|_2 \leq \delta$), the simple truncated Singular Value Decomposition of $\widehat{\mat A}$ produces a multiplicative approximation of $\mat A$ in Frobenius norm. This observation leads to many interesting results on general high-rank matrix estimation problems: 1.High-rank matrix completion: we show that it is possible to recover a {general high-rank matrix} $\mat A$ up to $(1+\varepsilon)$ relative error in Frobenius norm from partial observations, with sample complexity independent of the spectral gap of $\mat A$. 2.High-rank matrix denoising: we design algorithms that recovers a matrix $\mat A$ with relative error in Frobenius norm from its noise-perturbed observations, without assuming $\mat A$ is exactly low-rank. 3.Low-dimensional estimation of high-dimensional covariance: given $N$ i.i.d.~samples of dimension $n$ from $\mathcal N_n(\mat 0,\mat A)$, we show that it is possible to estimate the covariance matrix $\mat A$ with relative error in Frobenius norm with $N\approx n$,improving over classical covariance estimation results which requires $N\approx n^2$.

We study the problem of interactively learning a binary classifier using noisy labeling and pairwise comparison oracles, where the comparison oracle answers which one in the given two instances is more likely to be positive. Learning from such oracles has multiple applications where obtaining direct labels is harder but pairwise comparisons are easier, and the algorithm can leverage both types of oracles. In this paper, we attempt to characterize how the access to an easier comparison oracle helps in improving the label and total query complexity. We show that the comparison oracle reduces the learning problem to that of learning a threshold function. We then present an algorithm that interactively queries the label and comparison oracles and we characterize its query complexity under Tsybakov and adversarial noise conditions for the comparison and labeling oracles. Our lower bounds show that our label and total query complexity is almost optimal.

We derive computationally tractable methods to select a small subset of experiment settings from a large pool of given design points. The primary focus is on linear regression models, while the technique extends to generalized linear models and Delta's method (estimating functions of linear regression models) as well. The algorithms are based on a continuous relaxation of an otherwise intractable combinatorial optimization problem, with sampling or greedy procedures as post-processing steps. Formal approximation guarantees are established for both algorithms, and numerical results on both synthetic and real-world data confirm the effectiveness of the proposed methods.

We present a simple noise-robust margin-based active learn-ing algorithm to find homogeneous (passing the origin) linearseparators and analyze its error convergence when labels arecorrupted by noise. We show that when the imposed noisesatisfies the Tsybakov low noise condition (Mammen, Tsy-bakov, and others 1999; Tsybakov 2004) the algorithm is ableto adapt to unknown level of noise and achieves optimal sta-tistical rate up to polylogarithmic factors. We also derive lower bounds for margin based active learningalgorithms under Tsybakov noise conditions (TNC) for themembership query synthesis scenario (Angluin 1988). Ourresult implies lower bounds for the stream based selectivesampling scenario (Cohn 1990) under TNC for some fairlysimple data distributions. Quite surprisingly, we show that thesample complexity cannot be improved even if the underly-ing data distribution is as simple as the uniform distributionon the unit ball. Our proof involves the construction of a well-separated hypothesis set on the d-dimensional unit ball alongwith carefully designed label distributions for the Tsybakovnoise condition. Our analysis might provide insights for otherforms of lower bounds as well.

The problem of learning the structure of a high dimensional graphical model from data has received considerable attention in recent years. In many applications such as sensor networks and proteomics it is often expensive to obtain samples from all the variables involved simultaneously. For instance, this might involve the synchronization of a large number of sensors or the tagging of a large number of proteins. To address this important issue, we initiate the study of a novel graphical model selection problem, where the goal is to optimize the total number of scalar samples obtained by allowing the collection of samples from only subsets of the variables. We propose a general paradigm for graphical model selection where feedback is used to guide the sampling to high degree vertices, while obtaining only few samples from the ones with the low degrees. We instantiate this framework with two specific active learning algorithms, one of which makes mild assumptions but is computationally expensive, while the other is computationally more efficient but requires stronger (nevertheless standard) assumptions. Whereas the sample complexity of passive algorithms is typically a function of the maximum degree of the graph, we show that the sample complexity of our algorithms is provably smaller and that it depends on a novel local complexity measure that is akin to the average degree of the graph. We finally demonstrate the efficacy of our framework via simulations.

Subspace clustering is the problem of clustering data points into a union of low-dimensional linear/affine subspaces. It is the mathematical abstraction of many important problems in computer vision, image processing and machine learning. A line of recent work [4, 19, 24, 20] provided strong theoretical guarantee for sparse subspace cluster- ing [4], the state-of-the-art algorithm for sub- space clustering, on both noiseless and noisy data sets. It was shown that under mild conditions, with high probability no two points from different subspaces are clustered together. Such guarantee, however, is not sufficient for the clustering to be correct, due to the notorious “graph connectivity problem” [15]. In this paper, we investigate the graph connectivity problem for noisy sparse sub-space clustering and show that a simple post-processing procedure is capable of delivering consistent clustering under certain “general position” or “restricted eigenvalue” assumptions. We also show that our condition is almost tight with adversarial noise perturbation by constructing a counter-example. These results provide the first exact clustering guarantee of noisy SSC for subspaces of dimension greater then 3.

We study representations of piecewise-smooth signals on graphs. We first define classes for smooth, piecewise-constant, and piecewise-smooth graph signals, followed by a series of multiresolution local sets to analyze those signals by implementing a multiresolution analysis on graphs. Based on these local sets, we propose local-set-based piecewise-constant and piecewise-smooth dictionaries as graph signal representations that, in spirit, resemble the classical Haar wavelet basis and are naturally localized in both graph vertex and graph Fourier domains. Moreover, they promote sparsity when representing piecewise-smooth graph signals. In the experiments, we show that local-set-based dictionaries outperform graph Fourier domain based representations when approximating both simulated and real-world graph signals.

In this paper, we consider a statistical problem of learning a linear model from noisy samples. Existing work has focused on approximating the least squares solution by using leverage-based scores as an importance sampling distribution. However, no finite sample statistical guarantees and no computationally efficient optimal sampling strategies have been proposed. To evaluate the statistical properties of different sampling strategies, we propose a simple yet effective estimator, which is easy for theoretical analysis and is useful in multitask linear regression. We derive the exact mean square error of the proposed estimator for any given sampling scores. Based on minimizing the mean square error, we propose the optimal sampling scores for both estimator and predictor, and show that they are influenced by the noise-to-signal ratio. Numerical simulations match the theoretical analysis well.

Linear independence testing is a fundamental information-theoretic and statistical problem that can be posed as follows: given n points {(Xi, Yi)}i=1nfrom a p+q dimensional multivariate distribution where Xi∈ ℝpand Yi∈ ℝq, determine whether aTX and bTY are uncorrelated for every a ∈ ℝp; b ∈ ℝqor not. We give minimax lower bound for this problem (when p + q, n → ∞, (p + q)/n ≥ κXY∥F2for any procedure (test) to have non-trivial power, where ΣXYis the cross-covariance matrix of X, Y. We also provide evidence that the lower bound is tight, by connections to two-sample testing and regression when q = 1.

Recommendation and collaborative filtering systems are important in modern information and e-commerce applications. As these systems are becoming increasingly popular in industry, their outputs could affect business decision making, introducing incentives for an adversarial party to compromise the availability or integrity of such systems. We introduce a data poisoning attack on collaborative filtering systems. We demonstrate how a powerful attacker with full knowledge of the learner can generate malicious data so as to maximize his/her malicious objectives, while at the same time mimicking normal user behaviors to avoid being detected. While the complete knowledge assumption seems extreme, it enables a robust assessment of the vulnerability of collaborative filtering schemes to highly motivated attacks. We present efficient solutions for two popular factorization-based collaborative filtering algorithms: the alternative minimization formulation and the nuclear norm minimization method. Finally, we test the effectiveness of our proposed algorithms on real-world data and discuss potential defensive strategies.

Quantifying differences or similarities in connectomes has been a challenge due to the immense complexity of global brain networks. Here we introduce a noninvasive method that uses diffusion MRI to characterize whole-brain white matter architecture as a single local connectome fingerprint that allows for a direct comparison between structural connectomes. In four independently acquired data sets with repeated scans (total N = 213), we show that the local connectome fingerprint is highly specific to an individual, allowing for an accurate self-versus-others classification that achieved 100% accuracy across 17,398 identification tests. The estimated classification error was approximately one thousand times smaller than fingerprints derived from diffusivity-based measures or region-to-region connectivity patterns for repeat scans acquired within 3 months. The local connectome fingerprint also revealed neuroplasticity within an individual reflected as a decreasing trend in self-similarity across time, whereas this change was not observed in the diffusivity measures. Moreover, the local connectome fingerprint can be used as a phenotypic marker, revealing 12.51% similarity between monozygotic twins, 5.14% between dizygotic twins, and 4.51% between none-twin siblings, relative to differences between unrelated subjects. This novel approach opens a new door for probing the influence of pathological, genetic, social, or environmental factors on the unique configuration of the human connectome.

Summary Software development life cycle is a structured process, including the definition of user requirements specification, the system design, and programming. The design task comprises the transfer of natural language specifications into models. The class diagram of Unified Modeling Language has been considered as one of the most useful diagrams. It is a formal description of user's requirements and serves as inputs to the developers. The automated extraction of UML class diagram from natural language requirements is a highly challenging task. This paper explains our vision of an automated tool for class diagram generation from user requirements expressed in natural language. Our new approach amalgamates the statistical and pattern recognition properties of natural language processing techniques. More than 1000 patterns are defined for the extraction of the class diagram concepts. Once these concepts are captured, an XML Metadata Interchange file is generated and imported with a Computer‐Aided Software Engineering tool to build the corresponding UML class diagram. Copyright © 2015 John Wiley & Sons, Ltd.

This paper is about two related decision theoretic problems, nonparametric two-sample testing and independence testing. There is a belief that two recently proposed solutions, based on kernels and distances between pairs of points, behave well in high-dimensional settings. We identify different sources of misconception that give rise to the above belief. Specifically, we differentiate the hardness of estimation of test statistics from the hardness of testing whether these statistics are zero or not, and explicitly discuss a notion of "fair" alternative hypotheses for these problems as dimension increases. We then demonstrate that the power of these tests actually drops polynomially with increasing dimension against fair alternatives. We end with some theoretical insights and shed light on the median heuristic for kernel bandwidth selection. Our work advances the current understanding of the power of modern nonparametric hypothesis tests in high dimensions.

We consider the problem of clustering data points in high dimensions, i.e., when the number of data points may be much smaller than the number of dimensions. Specifically, we consider a Gaussian mixture model (GMM) with two non-spherical Gaussian components, where the clusters are distinguished by only a few relevant dimensions. The method we propose is a combination of a recent approach for learning parameters of a Gaussian mixture model and sparse linear discriminant analysis (LDA). In addition to cluster assignments, the method returns an estimate of the set of features relevant for clustering. Our results indicate that the sample complexity of clustering depends on the sparsity of the relevant feature set, while only scaling logarithmically with the ambient dimension. Further, we require much milder assumptions than existing work on clustering in high dimensions. In particular, we do not require spherical clusters nor necessitate mean separation along relevant dimensions.

Nonparametric two sample testing deals with the question of consistently deciding if two distributions are different, given samples from both, without making any parametric assumptions about the form of the distributions. The current literature is split into two kinds of tests - those which are consistent without any assumptions about how the distributions may differ (\textitgeneral alternatives), and those which are designed to specifically test easier alternatives, like a difference in means (\textitmean-shift alternatives). The main contribution of this paper is to explicitly characterize the power of a popular nonparametric two sample test, designed for general alternatives, under a mean-shift alternative in the high-dimensional setting. Specifically, we explicitly derive the power of the linear-time Maximum Mean Discrepancy statistic using the Gaussian kernel, where the dimension and sample size can both tend to infinity at any rate, and the two distributions differ in their means. As a corollary, we find that if the signal-to-noise ratio is held constant, then the test’s power goes to one if the number of samples increases faster than the dimension increases. This is the first explicit power derivation for a general nonparametric test in the high-dimensional setting, and the first analysis of how tests designed for general alternatives perform against easier ones.

Column subset selection of massive data matrices has found numerous applications in real-world data systems. In this paper, we propose and analyze two sampling based algorithms for column subset selection without access to the complete input matrix. To our knowledge, these are the first algorithms for column subset selection with missing data that are provably correct. The proposed methods work for row/column coherent matrices by employing the idea of adaptive sampling. Furthermore, when the input matrix has a noisy low-rank structure, one algorithm enjoys a relative error bound.

Subspace clustering groups data into several lowrank subspaces. In this paper, we propose a theoretical framework to analyze a popular optimization-based algorithm, Sparse Subspace Clustering (SSC), when the data dimension is compressed via some random projection algorithms. We show SSC provably succeeds if the random projection is a subspace embedding, which includes random Gaussian projection, uniform row sampling, FJLT, sketching, etc. Our analysis applies to the most general deterministic setting and is able to handle both adversarial and stochastic noise. It also results in the first algorithm for privacy-preserved subspace clustering.

Subspace clustering is an unsupervised learning problem that aims at grouping data points into multiple clusters'' so that data points in a single cluster lie approximately on a low-dimensional linear subspace. It is originally motivated by 3D motion segmentation in computer vision, but has recently been generically applied to a wide range of statistical machine learning problems, which often involves sensitive datasets about human subjects. This raises a dire concern for data privacy. In this work, we build on the framework ofdifferential privacy'' and present two provably private subspace clustering algorithms. We demonstrate via both theory and experiments that one of the presented methods enjoys formal privacy and utility guarantees; the other one asymptotically preserves differential privacy while having good performance in practice. Along the course of the proof, we also obtain two new provable guarantees for the agnostic subspace clustering and the graph connectivity problem which might be of independent interests.

We present the FuSSO, a functional analogue to the LASSO, that efficiently finds a sparse set of functional input covariates to regress a real-valued response against. The FuSSO does so in a semi-parametric fashion, making no parametric assumptions about the nature of input functional covariates and assuming a linear form to the mapping of functional covariates to the response. We provide a statistical backing for use of the FuSSO via proof of asymptotic sparsistency under various conditions. Furthermore, we observe good results on both synthetic and real-world data.

In active learning, the user sequentially chooses values for feature X and an oracle returns the corresponding label Y. In this paper, we consider the effect of feature noise in active learning, which could arise either because X itself is being measured, or it is corrupted in transmission to the oracle, or the oracle returns the label of a noisy version of the query point. In statistics, feature noise is known as“errors in variables” and has been studied extensively in non-active settings. However, the effect of feature noise in active learning has not been studied before. We consider the well-known Berkson errors-in-variables model with additive uniform noise of width σ. Our simple but revealing setting is that of one-dimensional binary classification setting where the goal is to learn a threshold (point where the probability of a + label crosses half). We deal with regression functions that are antisymmetric in a region of size σaround the threshold and also satisfy Tsybakov’s margin condition around the threshold. We prove minimax lower and upper bounds which demonstrate that when σis smaller than the minimiax active/passive noiseless error derived in Castro & Nowak (2007), then noise has no effect on the rates and one achieves the same noiseless rates. For larger σ, the \textitunflattening of the regression function on convolution with uniform noise, along with its local antisymmetry around the threshold, together yield a behaviour where noise \textitappears to be beneficial. Our key result is that active learning can buy significant improvement over a passive strategy even in the presence of feature noise.

Distribution regression refers to the situation where a response Y depends on a covariate P where P is a probability distribution. The model is Y=f(P) + e where f is an unknown regression function and e is a random error. Typically, we do not observe P directly, but rather, we observe a sample from P. In this paper we develop theory and methods for distribution-free versions of distribution regression. This means that we do not make strong distributional assumptions about the error term e and covariate P. We prove that when the effective dimension is small enough (as measured by the doubling dimension), then the excess prediction risk converges to zero with a polynomial rate.

We consider the detection of clusters of activation over graphs under Gaussian noise. This problem appears in many real world scenarios, such as the detecting contamination or seismic activity by sensor networks, viruses in human and computer networks, and groups with anomalous behavior in social and biological networks. Despite the wide applicability of such a detection algorithm, there has been little success in the development of computationally feasible methods with provable theoretical guarantees. To this end, we introduce the spanning tree wavelet basis over a graph, a localized basis that reflects the topology of the graph. We first provide a necessary condition for asymptotic distinguishability of the null and alternative hypotheses. Then we prove that for any spanning tree, we can hope to correctly detect signals in a low signal-to-noise regime using spanning tree wavelets. We propose a randomized test, in which we use a uniform spanning tree in the basis construction. Using electrical network theory, we show that the uniform spanning tree provides strong guarantees that in many cases match our necessary condition. We prove that for edge transitive graphs, k-nearest neighbor graphs, and ε-graphs we obtain nearly optimal performance with the uniform spanning tree wavelet detector.

We consider the change-point detection problem of deciding, based on noisy measurements, whether an unknown signal over a given graph is constant or is instead piecewise constant over two induced subgraphs of relatively low cut size. We analyze the corresponding generalized likelihood ratio (GLR) statistic and relate it to the problem of finding a sparsest cut in a graph. We develop a tractable relaxation of the GLR statistic based on the combinatorial Laplacian of the graph, which we call the spectral scan statistic, and analyze its properties. We show how its performance as a testing procedure depends directly on the spectrum of the graph, and use this result to explicitly derive its asymptotic properties on few graph topologies. Finally, we demonstrate both theoretically and by simulations that the spectral scan statistic can outperform naive testing procedures based on edge thresholding and χ^2 testing.

We focus on the problem of minimizing a convex function f over a convex set S given T queries to a stochastic first order oracle. We argue that the complexity of convex minimization is only determined by the rate of growth of the function around its minimum x^*_f,S, as quantified by a Tsybakov-like noise condition. Specifically, we prove that if f grows at least as fast as \|x-x^*_f,S\|^κaround its minimum, for some κ> 1, then the optimal rate of learning f(x^*_f,S) is Θ(T^-\fracκ2κ-2). The classic rate Θ(1/\sqrt T) for convex functions and Θ(1/T) for strongly convex functions are special cases of our result for κ→∞and κ=2, and even faster rates are attained for 1 < κ< 2. We also derive tight bounds for the complexity of learning x_f,S^*, where the optimal rate is Θ(T^-\frac12κ-2). Interestingly, these precise rates also characterize the complexity of active learning and our results further strengthen the connections between the fields of active learning and convex optimization, both of which rely on feedback-driven queries.

While several papers have investigated computationally and statistically efficient methods for learning Gaussian mixtures, precise minimax bounds for their statistical performance as well as fundamental limits in high-dimensional settings are not well-understood. In this paper, we provide precise information theoretic bounds on the clustering accuracy and sample complexity of learning a mixture of two isotropic Gaussians in high dimensions under small mean separation. If there is a sparse subset of relevant dimensions that determine the mean separation, then the sample complexity only depends on the number of relevant dimensions and mean separation, and can be achieved by a simple computationally efficient procedure. Our results provide the first step of a theoretical basis for recent methods that combine feature selection and clustering.

We investigate the problem of estimating the cluster tree for a density $f$ supported on or near a smooth $d$-dimensional manifold $M$ isometrically embedded in $\mathbb{R}^D$. We study a $k$-nearest neighbor based algorithm recently proposed by Chaudhuri and Dasgupta. Under mild assumptions on $f$ and $M$, we obtain rates of convergence that depend on $d$ only but not on the ambient dimension $D$. We also provide a sample complexity lower bound for a natural class of clustering algorithms that use $D$-dimensional neighborhoods.

We study low rank matrix and tensor completion and propose novel algorithms that employ adaptive sampling schemes to obtain strong performance guarantees for these problems. Our algorithms exploit adaptivity to identify entries that are highly informative for identifying the column space of the matrix (tensor) and consequently, our results hold even when the row space is highly coherent, in contrast with previous analysis of matrix completion. In the absence of noise, we show that one can exactly recover a $n \times n$ matrix of rank $r$ using $O(r^2 n \log(r))$ observations, which is better than the best known bound under random sampling. We also show that one can recover an order $T$ tensor using $O(r^{2(T-1)}T^2 n \log(r))$. For noisy recovery, we show that one can consistently estimate a low rank matrix corrupted with noise using $O(nr \textrm{polylog}(n))$ observations. We complement our study with simulations that verify our theoretical guarantees and demonstrate the scalability of our algorithms.

The detection of anomalous activity in graphs is a statistical problem that arises in many applications, such as network surveillance, disease outbreak detection, and activity monitoring in social networks. Beyond its wide applicability, graph structured anomaly detection serves as a case study in the difficulty of balancing computational complexity with statistical power. In this work, we develop from first principles the generalized likelihood ratio test for determining if there is a well connected region of activation over the vertices in the graph in Gaussian noise. Because this test is computationally infeasible, we provide a relaxation, called the Lov\'asz extended scan statistic (LESS) that uses submodularity to approximate the intractable generalized likelihood ratio. We demonstrate a connection between LESS and maximum a-posteriori inference in Markov random fields, which provides us with a poly-time algorithm for LESS. Using electrical network theory, we are able to control type 1 error for LESS and prove conditions under which LESS is risk consistent. Finally, we consider specific graph models, the torus, $k$-nearest neighbor graphs, and $\epsilon$-random graphs. We show that on these graphs our results provide near-optimal performance by matching our results to known lower bounds.

Knowledge of a network's topology and internal characteristics such as delay times or losses is crucial to maintain seamless operation of network services. Network tomography is a useful approach to infer such knowledge from end-to-end measurements between nodes at the periphery of the network, as it does not require cooperation of routers and other internal nodes. Most current tomography algorithms are single-source methods, which use multicast probes or synchronized unicast packet trains to measure covariances between destinations from a single vantage point and recover a tree topology from these measurements. Multi-source tomography, on the other hand, uses pairwise hop counts or latencies and consequently overcomes the difficulties associated with obtaining measurements for single-source methods. However, topology recovery is complicated by the fact that the paths along which measurements are taken do not form a tree in the network. Motivated by recent work suggesting that these measurements can be well-approximated by tree metrics, we present two algorithms that use selective pairwise distance measurements between peripheral nodes to construct a tree whose end-to-end distances approximate those in the network. Our first algorithm accommodates measurements perturbed by additive noise, while our second considers a novel noise model that captures missing measurements and the network's deviations from a tree topology. Both algorithms provably use O (p polylog p) pairwise measurements to construct a tree approximation on p end hosts. We present extensive simulated and real-world experiments to evaluate both of our algorithms.

Although spectral clustering has enjoyed considerable empirical success in machine learning, its theoretical properties are not yet fully developed. We analyze the performance of a spectral algorithm for hierarchical clustering and show that on a class of hierarchically structured similarity matrices, this algorithm can tolerate noise that grows with the number of data points while still perfectly recovering the hierarchical clusters with high probability. We additionally improve upon previous results for k-way spectral clustering to derive conditions under which spectral clustering makes no mistakes. Further, using minimax analysis, we derive tight upper and lower bounds for the clustering problem and compare the performance of spectral clustering to these information theoretic limits. We also present experiments on simulated and real world data illustrating our results.

We consider the problem of identifying a sparse set of relevant columns and rows in a large data matrix with highly corrupted entries. This problem of identifying groups from a collection of bipartite variables such as proteins and drugs, biological species and gene sequences, malware and signatures, etc is commonly referred to as biclustering or co-clustering. Despite its great practical relevance, and although several ad-hoc methods are available for biclustering, theoretical analysis of the problem is largely non-existent. The problem we consider is also closely related to structured multiple hypothesis testing, an area of statistics that has recently witnessed a flurry of activity. We make the following contributions: i) We prove lower bounds on the minimum signal strength needed for successful recovery of a bicluster as a function of the noise variance, size of the matrix and bicluster of interest. ii) We show that a combinatorial procedure based on the scan statistic achieves this optimal limit. iii) We characterize the SNR required by several computationally tractable procedures for biclustering including element-wise thresholding, column/row average thresholding and a convex relaxation approach to sparse singular vector decomposition.

We consider the problem of identifying an activation pattern in a complex, large-scale network that is embedded in very noisy measurements. This problem is relevant to several applications, such as identifying traces of a biochemical spread by a sensor network, expression levels of genes, and anomalous activity or congestion in the Internet. Extracting such patterns is a challenging task specially if the network is large (pattern is very high-dimensional) and the noise is so excessive that it masks the activity at any single node. However, typically there are statistical dependencies in the network activation process that can be leveraged to fuse the measurements of multiple nodes and enable reliable extraction of high-dimensional noisy patterns. In this paper, we analyze an estimator based on the graph Laplacian eigenbasis, and establish the limits of mean square error recovery of noisy patterns arising from a probabilistic (Gaussian or Ising) model based on an arbitrary graph structure. We consider both deterministic and probabilistic network evolution models, and our results indicate that by leveraging the network interaction structure, it is possible to consistently recover high-dimensional patterns even when the noise variance increases with network size.

Delay Tolerant Networks are increasingly being envisioned for a wide range of applications. Many of these applications need support for quality of service (QoS) differentiation from the network. This paper proposes a method for providing probabilistic delay assurances in DTNs. In particular, the paper presents a method called Delay- Differentiated Gossiping to assure a certain probability of meeting the packets' delay requirements while using as little network resources as possible. The idea is to adapt a set of forwarding probabilities and time-to-live parameters to control the usage of network resources based on how the delay requirements are being met. Empirical results evaluating the effectiveness of the proposed method are also included. The results show that there are simple ways of assuring the delay requirements while making effective use of the network resources.

Empirical evidence shows that in favorable situations semi-supervised learning (SSL) algorithms can capitalize on the abundancy of unlabeled training data to improve the performance of a learning task, in the sense that fewer labeled training data are needed to achieve a target error bound. However, in other situations unlabeled data do not seem to help. Recent attempts at theoretically characterizing the situations in which unlabeled data can help have met with little success, and sometimes appear to conflict with each other and intuition. In this paper, we attempt to bridge the gap between practice and theory of semi-supervised learning. We develop a rigorous framework for analyzing the situations in which unlabeled data can help and quantify the improvement possible using finite sample error bounds. We show that there are large classes of problems for which SSL can significantly outperform supervised learning, in finite sample regimes and sometimes also in terms of error convergence rates.

Comparative genomics provides a powerful tool for studying evolutionary changes among organisms, helping to identify genes that are conserved among species, as well as genes that give each organism its unique characteristics. However, the huge datasets involved makes this approach impractical on traditional computer architectures leading to prohibitively long runtimes. In this paper, we present a new computational grid architecture based on a hybrid computing model to significantly accelerate comparative genomics applications. The hybrid computing model consists of two types of parallelism: coarse grained and fine grained. The coarse-grained parallelism uses a volunteer computing infrastructure for job distribution, while the fine-grained parallelism uses commodity computer graphics hardware for fast sequence alignment. We present the deployment and evaluation of this approach on our grid test bed for the all-against-all comparison of microbial genomes. The results of this comparison are then used by phenotype--genotype explorer (PheGee). PheGee is a new tool that nominates candidate genes responsible for a given phenotype.

Developing energy efficient strategies for the extraction, transmission, and dissemination of information is a core theme in wireless sensor network research. In this paper we present a novel system for decentralized data compression and predistribution. The system simultaneously computes random projections of the sensor data and disseminates them throughout the network using a simple gossiping algorithm. These summary statistics are stored in an efficient manner and can be extracted from a small subset of nodes anywhere in the network. From these measurements one can reconstruct an accurate approximation of the data at all nodes in the network, provided the original data is compressible in a certain sense which need not be known to the nodes ahead of time. The system provides a practical and universal approach to decentralized compression and content distribution in wireless sensor networks. Two example applications, network health monitoring and field estimation, demonstrate the utility of our method.

This paper investigates data-adaptive path planning schemes for wireless networks of mobile sensor platforms. We focus on applications of environmental monitoring, in which the goal is to reconstruct a spatial map of environmental factors of interest. Traditional sampling theory deals with data collection processes that are completely independent of the target map to be estimated, aside from possible a priori specifications reflective of assumed properties of the target. We refer to such processes as passive learning methods. Alternatively, one can envision sequential, adaptive data collection procedures that use information gleaned from previous observations to guide the process. We refer to such feedback-driven processes as active learning methods. Active learning is naturally suited to mobile path planning, in which previous samples are used to guide the motion of the mobiles for further sampling. This paper presents some of the most encouraging theoretical results to date that support the effectiveness of active over passive learning, and focuses on new results regarding the capabilities of active learning methods for mobile sensing. Tradeoffs between latency, path lengths, and accuracy are carefully assessed using our theory. Adaptive path planning methods are developed to guide mobiles in order to focus attention in interesting regions of the sensing domain, thus conducting spatial surveys much more rapidly while maintaining the accuracy of the estimated map. The theory and methods are illustrated in the application of water current mapping in a freshwater lake.

Efficient medium access control in wireless networks has been a challenging task. While the IEEE 802.11 standard coordinates contention effectively, it severely limits the number of concurrent communications. This results in reduced throughput and efficiency. Recent research has focused on employing multiple antennas to increase throughput in a multipath environment by enabling multiple streams between a transmit-receive pair. In this paper we show that exploiting multiuser diversity to enable concurrent communications has certain advantages over multiple streaming. We propose a medium access control (MAC) protocol that uses adaptive interference cancellation with multiple antennas to increase network throughput and to provide better fairness, while requiring minimal change to the widely-deployed 802.11 MAC structure