Aarti Singh

AAAI Conference 2026 Conference Paper

Scaling Up AI Alignment

• Aarti Singh

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.

TMLR Journal 2025 Journal Article

Beyond Parameter Count: Implicit Bias in Soft Mixture of Experts

• Youngseog Chung
• Dhruv Malik
• Jeff Schneider
• Yuanzhi Li
• Aarti Singh

The traditional viewpoint on Sparse Mixture of Experts (MoE) models is that instead of training a single _large_ expert, which is computationally expensive, we can train many _small_ experts. The hope is that if the total parameter count of the small experts equals that of the singular large expert, then we retain the representation power of the large expert while gaining computational tractability and promoting expert specialization. The recently introduced Soft MoE replaces the Sparse MoE's discrete routing mechanism with a differentiable gating function that smoothly mixes tokens. While this smooth gating function successfully mitigates the various training instabilities associated with Sparse MoE, it is unclear whether it induces implicit biases that affect Soft MoE's representation power or potential for expert specialization. We prove that Soft MoE with a single arbitrarily powerful expert cannot represent simple convex functions. This justifies that Soft MoE's success cannot be explained by the traditional viewpoint of many small experts collectively mimicking the representation power of a single large expert, and that multiple experts are actually _necessary_ to achieve good representation power (even for a fixed total parameter count). Continuing along this line of investigation, we introduce a notion of expert specialization for Soft MoE, and while varying the number of experts yet fixing the total parameter count, we consider the following (computationally intractable) task. Given any input, how can we discover the expert subset that is specialized to predict this input's label? We empirically show that when there are many small experts, the architecture is implicitly biased in a fashion that allows us to efficiently approximate the specialized expert subset. Our method can be easily implemented to potentially reduce computation during inference. For example, using our method on ImageNet, one can perform inference using only $1/8$ of the experts and still retain $99$% of the test accuracy of using all experts.

ICML Conference 2025 Conference Paper

Data-driven Design of Randomized Control Trials with Guaranteed Treatment Effects

• Santiago Cortes-Gomez
• Naveen Janaki Raman
• Aarti Singh
• Bryan Wilder

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.

ICML Conference 2025 Conference Paper

Optimistic Algorithms for Adaptive Estimation of the Average Treatment Effect

• Ojash Neopane
• Aaditya Ramdas
• Aarti Singh

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.

ICML Conference 2025 Conference Paper

Projection Optimization: A General Framework for Multi-Objective and Multi-Group RLHF

• Nuoya Xiong
• Aarti Singh

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.

NeurIPS Conference 2025 Conference Paper

To Distill or Decide? Understanding the Algorithmic Trade-off in Partially Observable RL

• Yuda Song
• Dhruv Rohatgi
• Aarti Singh
• J. Bagnell

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.

NeurIPS Conference 2025 Conference Paper

Transformers Provably Learn Chain-of-Thought Reasoning with Length Generalization

• Yu Huang
• Zixin Wen
• Aarti Singh
• Yuejie Chi
• Yuxin Chen

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.

ICML Conference 2024 Conference Paper

Hybrid Reinforcement Learning from Offline Observation Alone

• Yuda Song 0001
• J. Andrew Bagnell
• Aarti Singh

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.

NeurIPS Conference 2024 Conference Paper

Learning Social Welfare Functions

• Kanad S. Pardeshi
• Itai Shapira
• Ariel D. Procaccia
• Aarti Singh

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.

ICLR Conference 2024 Conference Paper

Role of Locality and Weight Sharing in Image-Based Tasks: A Sample Complexity Separation between CNNs, LCNs, and FCNs

• Aakash Lahoti
• Stefani Karp
• Ezra Winston
• Aarti Singh
• Yuanzhi Li

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.

NeurIPS Conference 2024 Conference Paper

The Importance of Online Data: Understanding Preference Fine-tuning via Coverage

• Yuda Song
• Gokul Swamy
• Aarti Singh
• J. A. Bagnell
• Wen Sun

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.

ICML Conference 2023 Conference Paper

The Virtues of Laziness in Model-based RL: A Unified Objective and Algorithms

• Anirudh Vemula
• Yuda Song 0001
• Aarti Singh
• J. Andrew Bagnell
• Sanjiban Choudhury

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.

ICML Conference 2023 Conference Paper

Weighted Tallying Bandits: Overcoming Intractability via Repeated Exposure Optimality

• Dhruv Malik
• Conor Igoe
• Yuanzhi Li
• Aarti Singh

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.

TMLR Journal 2022 Journal Article

Integrating Rankings into Quantized Scores in Peer Review

• Yusha Liu
• Yichong Xu
• Nihar B Shah
• Aarti Singh

In peer review, reviewers are usually asked to provide scores for the papers. The scores are then used by Area Chairs or Program Chairs in various ways in the decision-making process. The scores are usually elicited in a quantized form to accommodate the limited cognitive ability of humans to describe their opinions in numerical values. It has been found that the quantized scores suffer from a large number of ties, thereby leading to a significant loss of information. To mitigate this issue, conferences have started to ask reviewers to additionally provide a ranking of the papers they have reviewed. There are however two key challenges. First, there is no standard procedure for using this ranking information and Area Chairs may use it in different ways (including simply ignoring them), thereby leading to arbitrariness in the peer-review process. Second, there are no suitable interfaces for judicious use of this data nor methods to incorporate it in existing workflows, thereby leading to inefficiencies. We take a principled approach to integrate the ranking information into the scores. The output of our method is an updated score pertaining to each review that also incorporates the rankings. Our approach addresses the two aforementioned challenges by: (i) ensuring that rankings are incorporated into the updated scores in the same manner for all papers, thereby mitigating arbitrariness, and (ii) allowing to seamlessly use existing interfaces and workflows designed for scores. We empirically evaluate our method on synthetic datasets as well as on peer reviews from the ICLR 2017 conference, and find that it reduces the error by approximately 30% as compared to the best performing baseline on the ICLR 2017 data.

JMLR Journal 2022 Journal Article

Two-Sample Testing on Ranked Preference Data and the Role of Modeling Assumptions

• Charvi Rastogi
• Sivaraman Balakrishnan
• Nihar B. Shah
• Aarti Singh

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. [abs] [ pdf ][ bib ] &copy JMLR 2022. ( edit, beta )

AAAI Conference 2021 Conference Paper

A Novice-Reviewer Experiment to Address Scarcity of Qualified Reviewers in Large Conferences

• Ivan Stelmakh
• Nihar B. Shah
• Aarti Singh
• Hal Daumé III

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).

AAAI Conference 2021 Conference Paper

Catch Me if I Can: Detecting Strategic Behaviour in Peer Assessment

• Ivan Stelmakh
• Nihar B. Shah
• Aarti Singh

We consider the issue of strategic behaviour in various peerassessment tasks, including peer grading of exams or homeworks and peer review in hiring or promotions. When a peerassessment 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.

NeurIPS Conference 2021 Conference Paper

Local Signal Adaptivity: Provable Feature Learning in Neural Networks Beyond Kernels

• Stefani Karp
• Ezra Winston
• Yuanzhi Li
• Aarti Singh

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.

JMLR Journal 2021 Journal Article

PeerReview4All: Fair and Accurate Reviewer Assignment in Peer Review

• Ivan Stelmakh
• Nihar Shah
• Aarti Singh

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. [abs] [ pdf ][ bib ] &copy JMLR 2021. ( edit, beta )

NeurIPS Conference 2020 Conference Paper

Preference-based Reinforcement Learning with Finite-Time Guarantees

• Yichong Xu
• Ruosong Wang
• Lin Yang
• Aarti Singh
• Artur Dubrawski

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.

JMLR Journal 2020 Journal Article

Regression with Comparisons: Escaping the Curse of Dimensionality with Ordinal Information

• Yichong Xu
• Sivaraman Balakrishnan
• Aarti Singh
• Artur Dubrawski

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. [abs] [ pdf ][ bib ] &copy JMLR 2020. ( edit, beta )

UAI Conference 2020 Conference Paper

Zeroth Order Non-convex optimization with Dueling-Choice Bandits

• Yichong Xu
• Aparna Joshi
• Aarti Singh
• Artur Dubrawski

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.

NeurIPS Conference 2019 Conference Paper

On Testing for Biases in Peer Review

• Ivan Stelmakh
• Nihar Shah
• Aarti Singh

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.

ICML Conference 2018 Conference Paper

Gradient Descent Learns One-hidden-layer CNN: Don't be Afraid of Spurious Local Minima

• Simon S. Du
• Jason D. Lee
• Yuandong Tian
• Aarti Singh
• Barnabás Póczos

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.

NeurIPS Conference 2018 Conference Paper

How Many Samples are Needed to Estimate a Convolutional Neural Network?

• Simon Du
• Yining Wang
• Xiyu Zhai
• Sivaraman Balakrishnan
• Russ Salakhutdinov
• Aarti Singh

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.

ICML Conference 2018 Conference Paper

Nonparametric Regression with Comparisons: Escaping the Curse of Dimensionality with Ordinal Information

• Yichong Xu
• Hariank Muthakana
• Sivaraman Balakrishnan
• Aarti Singh
• Artur Dubrawski

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.

NeurIPS Conference 2018 Conference Paper

Optimization of Smooth Functions with Noisy Observations: Local Minimax Rates

• Yining Wang
• Sivaraman Balakrishnan
• Aarti Singh

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.

JMLR Journal 2018 Journal Article

Provably Correct Algorithms for Matrix Column Subset Selection with Selectively Sampled Data

• Yining Wang
• Aarti Singh

We consider the problem of matrix column subset selection, which selects a subset of columns from an input matrix such that the input can be well approximated by the span of the selected columns. Column subset selection has been applied to numerous real-world data applications such as population genetics summarization, electronic circuits testing and recommendation systems. In many applications the complete data matrix is unavailable and one needs to select representative columns by inspecting only a small portion of the input matrix. In this paper we propose the first provably correct column subset selection algorithms for partially observed data matrices. Our proposed algorithms exhibit different merits and limitations in terms of statistical accuracy, computational efficiency, sample complexity and sampling schemes, which provides a nice exploration of the tradeoff between these desired properties for column subset selection. The proposed methods employ the idea of feedback driven sampling and are inspired by several sampling schemes previously introduced for low-rank matrix approximation tasks (Drineas et al., 2008; Frieze et al., 2004; Deshpande and Vempala, 2006; Krishnamurthy and Singh, 2014). Our analysis shows that, under the assumption that the input data matrix has incoherent rows but possibly coherent columns, all algorithms provably converge to the best low-rank approximation of the original data as number of selected columns increases. Furthermore, two of the proposed algorithms enjoy a relative error bound, which is preferred for column subset selection and matrix approximation purposes. We also demonstrate through both theoretical and empirical analysis the power of feedback driven sampling compared to uniform random sampling on input matrices with highly correlated columns. [abs] [ pdf ][ bib ] &copy JMLR 2018. ( edit, beta )

NeurIPS Conference 2017 Conference Paper

Gradient Descent Can Take Exponential Time to Escape Saddle Points

• Simon Du
• Chi Jin
• Jason Lee
• Michael Jordan
• Aarti Singh
• Barnabas Poczos

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.

NeurIPS Conference 2017 Conference Paper

Hypothesis Transfer Learning via Transformation Functions

• Simon Du
• Jayanth Koushik
• Aarti Singh
• Barnabas Poczos

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.

ICML Conference 2017 Conference Paper

Near-Optimal Design of Experiments via Regret Minimization

• Zeyuan Allen-Zhu
• Yuanzhi Li
• Aarti Singh
• Yining Wang 0001

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.

NeurIPS Conference 2017 Conference Paper

Noise-Tolerant Interactive Learning Using Pairwise Comparisons

• Yichong Xu
• Hongyang Zhang
• Kyle Miller
• Aarti Singh
• Artur Dubrawski

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.

JMLR Journal 2017 Journal Article

On Computationally Tractable Selection of Experiments in Measurement-Constrained Regression Models

• Yining Wang
• Adams Wei Yu
• Aarti Singh

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. [abs] [ pdf ][ bib ] &copy JMLR 2017. ( edit, beta )

NeurIPS Conference 2017 Conference Paper

On the Power of Truncated SVD for General High-rank Matrix Estimation Problems

• Simon Du
• Yining Wang
• Aarti Singh

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 $N\approx n^2$.

ICML Conference 2017 Conference Paper

Uncorrelation and Evenness: a New Diversity-Promoting Regularizer

• Pengtao Xie
• Aarti Singh
• Eric P. Xing

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.

NeurIPS Conference 2016 Conference Paper

Data Poisoning Attacks on Factorization-Based Collaborative Filtering

• Bo Li
• Yining Wang
• Aarti Singh
• Yevgeniy Vorobeychik

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.

AAAI Conference 2016 Conference Paper

Noise-Adaptive Margin-Based Active Learning and Lower Bounds under Tsybakov Noise Condition

• Yining Wang
• Aarti Singh

We present a simple noise-robust margin-based active learning algorithm to find homogeneous (passing the origin) linear separators and analyze its error convergence when labels are corrupted by noise. We show that when the imposed noise satisfies the Tsybakov low noise condition (Mammen, Tsybakov, and others 1999; Tsybakov 2004) the algorithm is able to adapt to unknown level of noise and achieves optimal statistical rate up to polylogarithmic factors. We also derive lower bounds for margin based active learning algorithms under Tsybakov noise conditions (TNC) for the membership query synthesis scenario (Angluin 1988). Our result implies lower bounds for the stream based selective sampling scenario (Cohn 1990) under TNC for some fairly simple data distributions. Quite surprisingly, we show that the sample complexity cannot be improved even if the underlying data distribution is as simple as the uniform distribution on the unit ball. Our proof involves the construction of a wellseparated hypothesis set on the d-dimensional unit ball along with carefully designed label distributions for the Tsybakov noise condition. Our analysis might provide insights for other forms of lower bounds as well.

ICML Conference 2015 Conference Paper

A Deterministic Analysis of Noisy Sparse Subspace Clustering for Dimensionality-reduced Data

• Yining Wang 0001
• Yu-Xiang Wang 0003
• Aarti Singh

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.

NeurIPS Conference 2015 Conference Paper

Differentially private subspace clustering

• Yining Wang
• Yu-Xiang Wang
• Aarti Singh

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 of differential 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.

AAAI Conference 2015 Conference Paper

On the Decreasing Power of Kernel and Distance Based Nonparametric Hypothesis Tests in High Dimensions

• Aaditya Ramdas
• Sashank Jakkam Reddi
• Barnabas Poczos
• Aarti Singh
• Larry Wasserman

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.

NeurIPS Conference 2013 Conference Paper

Cluster Trees on Manifolds

• Sivaraman Balakrishnan
• Srivatsan Narayanan
• Alessandro Rinaldo
• Aarti Singh
• Larry Wasserman

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.

NeurIPS Conference 2013 Conference Paper

Low-Rank Matrix and Tensor Completion via Adaptive Sampling

• Akshay Krishnamurthy
• Aarti Singh

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.

NeurIPS Conference 2013 Conference Paper

Minimax Theory for High-dimensional Gaussian Mixtures with Sparse Mean Separation

• Martin Azizyan
• Aarti Singh
• Larry Wasserman

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.

NeurIPS Conference 2013 Conference Paper

Near-optimal Anomaly Detection in Graphs using Lovasz Extended Scan Statistic

• James Sharpnack
• Akshay Krishnamurthy
• Aarti Singh

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.

ICML Conference 2013 Conference Paper

Optimal rates for stochastic convex optimization under Tsybakov noise condition

• Aaditya Ramdas
• Aarti Singh

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.

ICML Conference 2012 Conference Paper

Efficient Active Algorithms for Hierarchical Clustering

• Akshay Krishnamurthy
• Sivaraman Balakrishnan
• Min Xu 0010
• Aarti Singh

JMLR Journal 2012 Journal Article

Stability of Density-Based Clustering

• Alessandro Rinaldo
• Aarti Singh
• Rebecca Nugent
• Larry Wasserman

High density clusters can be characterized by the connected components of a level set L(λ) = {x: p(x)>λ} of the underlying probability density function p generating the data, at some appropriate level λ ≥ 0. The complete hierarchical clustering can be characterized by a cluster tree T= ∪ λ L(λ). In this paper, we study the behavior of a density level set estimate L̂(λ) and cluster tree estimate T̂ based on a kernel density estimator with kernel bandwidth h. We define two notions of instability to measure the variability of L̂(λ) and T̂ as a function of h, and investigate the theoretical properties of these instability measures. [abs] [ pdf ][ bib ] &copy JMLR 2012. ( edit, beta )

NeurIPS Conference 2011 Conference Paper

Minimax Localization of Structural Information in Large Noisy Matrices

• Mladen Kolar
• Sivaraman Balakrishnan
• Alessandro Rinaldo
• Aarti Singh

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.

NeurIPS Conference 2011 Conference Paper

Noise Thresholds for Spectral Clustering

• Sivaraman Balakrishnan
• Min Xu
• Akshay Krishnamurthy
• Aarti Singh

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.

NeurIPS Conference 2010 Conference Paper

Identifying graph-structured activation patterns in networks

• James Sharpnack
• Aarti Singh

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.

NeurIPS Conference 2008 Conference Paper

Unlabeled data: Now it helps, now it doesn't

• Aarti Singh
• Robert Nowak
• Jerry Zhu

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.