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Vatsal Sharan

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25 papers

2 author rows

AAAI Conference 2026 Conference Paper

An External Fairness Evaluation of LinkedIn Talent Search

Tina Behzad
Siddartha Devic
Vatsal Sharan
Aleksandra Korolova
David Kempe

We conduct an independent, third-party audit for bias of LinkedIn's Talent Search ranking system, focusing on potential ranking bias across two attributes: gender and race. To do so, we first construct a dataset of rankings produced by the system, collecting extensive Talent Search results across a diverse set of occupational queries. We then develop a robust labeling pipeline that infers the two demographic attributes of interest for the returned users. To evaluate potential biases in the collected dataset of real-world rankings, we utilize two exposure disparity metrics: deviation from group proportions and MinSkew@k. Our analysis reveals an under-representation of minority groups in early ranks across many queries. We further examine potential causes of this disparity, and discuss why they may be difficult or, in some cases, impossible to fully eliminate among the early ranks of queries. Beyond static metrics, we also investigate the concept of subgroup fairness over time, highlighting \emph{temporal disparities} in exposure and retention, which are often more difficult to audit for in practice. In employer recruiting platforms such as LinkedIn Talent Search, the persistence of a particular candidate over multiple days in the ranking can directly impact the probability that the given candidate is selected for opportunities. Our analysis reveals demographic disparities in this temporal stability, with some groups experiencing greater volatility in their ranked positions than others. We contextualize all our findings alongside LinkedIn’s published self-audits of its Talent Search system and reflect on the methodological constraints of a black-box external evaluation, including limited observability and noisy demographic inference. Our work contributes empirical insights and practical guidance for conducting third-party audits of modern socio-technical systems which go beyond the well-studied and standard algorithmic fairness guarantees of predictors.

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NeurIPS Conference 2025 Conference Paper

Discovering Data Structures: Nearest Neighbor Search and Beyond

Omar Salemohamed
Laurent Charlin
Shivam Garg
Vatsal Sharan
Gregory Valiant

We explore if it is possible to learn data structures end-to-end with neural networks, with a focus on the problem of nearest-neighbor (NN) search. We introduce a framework for data structure discovery, which adapts to the underlying data distribution and provides fine-grained control over query and space complexity. Crucially, the data structure is learned from scratch, and does not require careful initialization or seeding with candidate data structures. In several settings, we are able to reverse-engineer the learned data structures and query algorithms. For 1D nearest neighbor search, the model discovers optimal distribution (in)dependent algorithms such as binary search and variants of interpolation search. In higher dimensions, the model learns solutions that resemble k-d trees in some regimes, while in others, elements of locality-sensitive hashing emerge. Additionally, the model learns useful representations of high-dimensional data such as images and exploits them to design effective data structures. Beyond NN search, we believe the framework could be a powerful tool for data structure discovery for other problems and adapt our framework to the problem of estimating frequencies over a data stream. To encourage future work in this direction, we conclude with a discussion on some of the opportunities and remaining challenges of learning data structures end-to-end.

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NeurIPS Conference 2025 Conference Paper

Improved Bounds for Swap Multicalibration and Swap Omniprediction

Haipeng Luo
Spandan Senapati
Vatsal Sharan

In this paper, we consider the related problems of multicalibration --- a multigroup fairness notion and omniprediction --- a simultaneous loss minimization paradigm, both in the distributional and online settings. The recent work of Garg et al. (2024) raised the open problem of whether it is possible to efficiently achieve $\tilde{\mathcal{O}}(\sqrt{T})$ $\ell_{2}$-multicalibration error against bounded linear functions. In this paper, we answer this question in a strongly affirmative sense. We propose an efficient algorithm that achieves $\tilde{\mathcal{O}}(T^{\frac{1}{3}})$ $\ell_{2}$-swap multicalibration error (both in high probability and expectation). On propagating this bound onward, we obtain significantly improved rates for $\ell_{1}$-swap multicalibration and swap omniprediction for a loss class of convex Lipschitz functions. In particular, we show that our algorithm achieves $\tilde{\mathcal{O}}(T^{\frac{2}{3}})$ $\ell_{1}$-swap multicalibration and swap omniprediction errors, thereby improving upon the previous best-known bound of $\tilde{\mathcal{O}}(T^{\frac{7}{8}})$. As a consequence of our improved online results, we further obtain several improved sample complexity rates in the distributional setting. In particular, we establish a $\tilde{\mathcal{O}}(\varepsilon ^ {-3})$ sample complexity of efficiently learning an $\varepsilon$-swap omnipredictor for the class of convex and Lipschitz functions, $\tilde{\mathcal{O}}(\varepsilon ^{-2. 5})$ sample complexity of efficiently learning an $\varepsilon$-swap agnostic learner for the squared loss, and $\tilde{\mathcal{O}}(\varepsilon ^ {-5}), \tilde{\mathcal{O}}(\varepsilon ^ {-2. 5})$ sample complexities of learning $\ell_{1}, \ell_{2}$-swap multicalibrated predictors against linear functions, all of which significantly improve on the previous best-known bounds.

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NeurIPS Conference 2025 Conference Paper

Simultaneous Swap Regret Minimization via KL-Calibration

Haipeng Luo
Spandan Senapati
Vatsal Sharan

Calibration is a fundamental concept that aims at ensuring the reliability of probabilistic predictions by aligning them with real-world outcomes. There is a surge of studies on new calibration measures that are easier to optimize compared to the classical $\ell_1$-Calibration while still having strong implications for downstream applications. One recent such example is the work by Fishelson et al. (2025) who show that it is possible to achieve $\tilde{\mathcal{O}}(T^{1/3})$ pseudo $\ell_{2}$-Calibration error via minimizing pseudo swap regret of the squared loss, which in fact implies the same bound for all bounded proper losses with a smooth univariate form. In this work, we significantly generalize their result in the following ways: (a) in addition to smooth univariate forms, our algorithm also simultaneously achieves $\tilde{\mathcal{O}}(T^{1/3})$ swap regret for any proper loss with a twice continuously differentiable univariate form (such as Tsallis entropy); (b) our bounds hold not only for pseudo swap regret that measures losses using the forecaster's distributions on predictions, but also hold for the actual swap regret that measures losses using the forecaster's actual realized predictions. We achieve so by introducing a new stronger notion of calibration called (pseudo) KL-Calibration, which we show is equivalent to the (pseudo) swap regret with respect to log loss. We prove that there exists an algorithm that achieves $\tilde{\mathcal{O}}(T^{1/3})$ KL-Calibration error and provide an explicit algorithm that achieves $\tilde{\mathcal{O}}(T^{1/3})$ pseudo KL-Calibration error. Moreover, we show that the same algorithm achieves ${\mathcal{O}}(T^{1/3} (\log T) ^ {-\frac{1}{3}}\log (T/{\delta}))$ swap regret with probability at least $1-\delta$ for any proper loss with a smooth univariate form, which implies $\tilde{\mathcal{O}}(T^{1/3})$ $\ell_2$-Calibration error. A technical contribution of our work is a new randomized rounding procedure and a non-uniform discretization scheme to minimize the swap regret for log loss.

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NeurIPS Conference 2025 Conference Paper

The Rich and the Simple: On the Implicit Bias of Adam and SGD

Bhavya Vasudeva
Jung Lee
Vatsal Sharan
Mahdi Soltanolkotabi

Adam is the de facto optimization algorithm for several deep learning applications, but an understanding of its implicit bias and how it differs from other algorithms, particularly standard first-order methods such as (stochastic) gradient descent (GD), remains limited. In practice, neural networks (NNs) trained with SGD are known to exhibit simplicity bias --- a tendency to find simple solutions. In contrast, we show that Adam is more resistant to such simplicity bias. First, we investigate the differences in the implicit biases of Adam and GD when training two-layer ReLU NNs on a binary classification task with Gaussian data. We find that GD exhibits a simplicity bias, resulting in a linear decision boundary with a suboptimal margin, whereas Adam leads to much richer and more diverse features, producing a nonlinear boundary that is closer to the Bayes' optimal predictor. This richer decision boundary also allows Adam to achieve higher test accuracy both in-distribution and under certain distribution shifts. We theoretically prove these results by analyzing the population gradients. Next, to corroborate our theoretical findings, we present extensive empirical results showing that this property of Adam leads to superior generalization across various datasets with spurious correlations where NNs trained with SGD are known to show simplicity bias and do not generalize well under certain distributional shifts.

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ICLR Conference 2025 Conference Paper

Transformers Learn Low Sensitivity Functions: Investigations and Implications

Bhavya Vasudeva
Deqing Fu
Tianyi Zhou 0011
Elliott Kau
Youqi Huang
Vatsal Sharan

Transformers achieve state-of-the-art accuracy and robustness across many tasks, but an understanding of their inductive biases and how those biases differ from other neural network architectures remains elusive. In this work, we identify the sensitivity of the model to token-wise random perturbations in the input as a unified metric which explains the inductive bias of transformers across different data modalities and distinguishes them from other architectures. We show that transformers have lower sensitivity than MLPs, CNNs, ConvMixers and LSTMs, across both vision and language tasks. We also show that this low-sensitivity bias has important implications: i) lower sensitivity correlates with improved robustness; it can also be used as an efficient intervention to further improve the robustness of transformers; ii) it corresponds to flatter minima in the loss landscape; and iii) it can serve as a progress measure for grokking. We support these findings with theoretical results showing (weak) spectral bias of transformers in the NTK regime, and improved robustness due to the lower sensitivity.

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TMLR Journal 2024 Journal Article

Mitigating Simplicity Bias in Deep Learning for Improved OOD Generalization and Robustness

Bhavya Vasudeva
Kameron Shahabi
Vatsal Sharan

Neural networks (NNs) are known to exhibit simplicity bias where they tend to prefer learning 'simple' features over more 'complex' ones, even when the latter may be more informative. Simplicity bias can lead to the model making biased predictions which have poor out-of-distribution (OOD) generalization and subgroup robustness. To address this, we propose a hypothesis about spurious features that directly connects to simplicity bias: we hypothesize that spurious features on many datasets are simple features that are still predictive of the label. We empirically validate this hypothesis, and subsequently develop a framework which leverages this hypothesis to learn more robust models. In our proposed framework, we first train a simple model, and then regularize the conditional mutual information with respect to it to obtain the final model. We theoretically study the effect of this regularization and show that it provably reduces reliance on spurious features in certain settings. We also empirically demonstrate the effectiveness of this framework in various problem settings and real-world applications, showing that it effectively addresses simplicity bias and leads to more features being used, enhances OOD generalization, and improves subgroup robustness and fairness.

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NeurIPS Conference 2024 Conference Paper

Optimal Multiclass U-Calibration Error and Beyond

Haipeng Luo
Spandan Senapati
Vatsal Sharan

We consider the problem of online multiclass U-calibration, where a forecaster aims to make sequential distributional predictions over $K$ classes with low U-calibration error, that is, low regret with respect to all bounded proper losses simultaneously. Kleinberg et al. (2023) developed an algorithm with U-calibration error $\mathcal{O}(K\sqrt{T})$ after $T$ rounds and raised the open question of what the optimal bound is. We resolve this question by showing that the optimal U-calibration error is $\Theta(\sqrt{KT})$ --- we start with a simple observation that the Follow-the-Perturbed-Leader algorithm of Daskalakis and Syrgkanis (2016) achieves this upper bound, followed by a matching lower bound constructed with a specific proper loss (which, as a side result, also proves the optimality of the algorithm of Daskalakis and Syrgkanis (2016) in the context of online learning against an adversary with finite choices). We also strengthen our results under natural assumptions on the loss functions, including $\Theta(\log T)$ U-calibration error for Lipschitz proper losses, $\mathcal{O}(\log T)$ U-calibration error for a certain class of decomposable proper losses, U-calibration error bounds for proper losses with a low covering number, and others.

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NeurIPS Conference 2024 Conference Paper

Pre-trained Large Language Models Use Fourier Features to Compute Addition

Tianyi Zhou
Deqing Fu
Vatsal Sharan
Robin Jia

Pre-trained large language models (LLMs) exhibit impressive mathematical reasoning capabilities, yet how they compute basic arithmetic, such as addition, remains unclear. This paper shows that pre-trained LLMs add numbers using Fourier features---dimensions in the hidden state that represent numbers via a set of features sparse in the frequency domain. Within the model, MLP and attention layers use Fourier features in complementary ways: MLP layers primarily approximate the magnitude of the answer using low-frequency features, while attention layers primarily perform modular addition (e. g. , computing whether the answer is even or odd) using high-frequency features. Pre-training is crucial for this mechanism: models trained from scratch to add numbers only exploit low-frequency features, leading to lower accuracy. Introducing pre-trained token embeddings to a randomly initialized model rescues its performance. Overall, our analysis demonstrates that appropriate pre-trained representations (e. g. , Fourier features) can unlock the ability of Transformers to learn precise mechanisms for algorithmic tasks.

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ICML Conference 2024 Conference Paper

Stability and Multigroup Fairness in Ranking with Uncertain Predictions

Siddartha Devic
Aleksandra Korolova
David Kempe 0001
Vatsal Sharan

Rankings are ubiquitous across many applications, from search engines to hiring committees. In practice, many rankings are derived from the output of predictors. However, when predictors trained for classification tasks have intrinsic uncertainty, it is not obvious how this uncertainty should be represented in the derived rankings. Our work considers ranking functions: maps from individual predictions for a classification task to distributions over rankings. We focus on two aspects of ranking functions: stability to perturbations in predictions and fairness towards both individuals and subgroups. Not only is stability an important requirement for its own sake, but — as we show — it composes harmoniously with individual fairness in the sense of Dwork et al. (2012). While deterministic ranking functions cannot be stable aside from trivial scenarios, we show that the recently proposed uncertainty aware (UA) ranking functions of Singh et al. (2021) are stable. Our main result is that UA rankings also achieve group fairness through successful composition with multiaccurate or multicalibrated predictors. Our work demonstrates that UA rankings naturally interpolate between group and individual level fairness guarantees, while simultaneously satisfying stability guarantees important whenever machine-learned predictions are used.

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NeurIPS Conference 2024 Conference Paper

Transductive Learning is Compact

Julian Asilis
Siddartha Devic
Shaddin Dughmi
Vatsal Sharan
Shang-Hua Teng

We demonstrate a compactness result holding broadly across supervised learning with a general class of loss functions: Any hypothesis class $\mathcal{H}$ is learnable with transductive sample complexity $m$ precisely when all of its finite projections are learnable with sample complexity $m$. We prove that this exact form of compactness holds for realizable and agnostic learning with respect to all proper metric loss functions (e. g. , any norm on $\mathbb{R}^d$) and any continuous loss on a compact space (e. g. , cross-entropy, squared loss). For realizable learning with improper metric losses, we show that exact compactness of sample complexity can fail, and provide matching upper and lower bounds of a factor of 2 on the extent to which such sample complexities can differ. We conjecture that larger gaps are possible for the agnostic case. Furthermore, invoking the equivalence between sample complexities in the PAC and transductive models (up to lower order factors, in the realizable case) permits us to directly port our results to the PAC model, revealing an almost-exact form of compactness holding broadly in PAC learning.

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NeurIPS Conference 2024 Conference Paper

Transformers Learn to Achieve Second-Order Convergence Rates for In-Context Linear Regression

Deqing Fu
Tian-Qi Chen
Robin Jia
Vatsal Sharan

Transformers excel at *in-context learning* (ICL)---learning from demonstrations without parameter updates---but how they do so remains a mystery. Recent work suggests that Transformers may internally run Gradient Descent (GD), a first-order optimization method, to perform ICL. In this paper, we instead demonstrate that Transformers learn to approximate second-order optimization methods for ICL. For in-context linear regression, Transformers share a similar convergence rate as *Iterative Newton's Method*, both *exponentially* faster than GD. Empirically, predictions from successive Transformer layers closely match different iterations of Newton’s Method linearly, with each middle layer roughly computing 3 iterations; thus, Transformers and Newton’s method converge at roughly the same rate. In contrast, Gradient Descent converges exponentially more slowly. We also show that Transformers can learn in-context on ill-conditioned data, a setting where Gradient Descent struggles but Iterative Newton succeeds. Finally, to corroborate our empirical findings, we prove that Transformers can implement $k$ iterations of Newton's method with $k + \mathcal O(1)$ layers.

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NeurIPS Conference 2024 Conference Paper

When is Multicalibration Post-Processing Necessary?

Dutch Hansen
Siddartha Devic
Preetum Nakkiran
Vatsal Sharan

Calibration is a well-studied property of predictors which guarantees meaningful uncertainty estimates. Multicalibration is a related notion --- originating in algorithmic fairness --- which requires predictors to be simultaneously calibrated over a potentially complex and overlapping collection of protected subpopulations (such as groups defined by ethnicity, race, or income). We conduct the first comprehensive study evaluating the usefulness of multicalibration post-processing across a broad set of tabular, image, and language datasets for models spanning from simple decision trees to 90 million parameter fine-tuned LLMs. Our findings can be summarized as follows: (1) models which are calibrated out of the box tend to be relatively multicalibrated without any additional post-processing; (2) multicalibration can help inherently uncalibrated models and also large vision and language models; and (3) traditional calibration measures may sometimes provide multicalibration implicitly. More generally, we also distill many independent observations which may be useful for practical and effective applications of multicalibration post-processing in real-world contexts.

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IJCAI Conference 2023 Conference Paper

Efficient Convex Optimization Requires Superlinear Memory (Extended Abstract)

Annie Marsden
Vatsal Sharan
Aaron Sidford
Gregory Valiant

Minimizing a convex function with access to a first order oracle---that returns the function evaluation and (sub)gradient at a query point---is a canonical optimization problem and a fundamental primitive in machine learning. Gradient-based methods are the most popular approaches used for solving the problem, owing to their simplicity and computational efficiency. These methods, however, do not achieve the information-theoretically optimal query complexity for minimizing the underlying function to small error, which are achieved by more expensive techniques based on cutting-plane methods. Is it possible to achieve the information-theoretically query complexity without using these more complex and computationally expensive methods? In this work, we use memory as a lens to understand this, and show that is is not possible to achieve optimal query complexity without using significantly more memory than that used by gradient descent.

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ICML Conference 2023 Conference Paper

Fairness in Matching under Uncertainty

Siddartha Devic
David Kempe 0001
Vatsal Sharan
Aleksandra Korolova

The prevalence and importance of algorithmic two-sided marketplaces has drawn attention to the issue of fairness in such settings. Algorithmic decisions are used in assigning students to schools, users to advertisers, and applicants to job interviews. These decisions should heed the preferences of individuals, and simultaneously be fair with respect to their merits (synonymous with fit, future performance, or need). Merits conditioned on observable features are always uncertain, a fact that is exacerbated by the widespread use of machine learning algorithms to infer merit from the observables. As our key contribution, we carefully axiomatize a notion of individual fairness in the two-sided marketplace setting which respects the uncertainty in the merits; indeed, it simultaneously recognizes uncertainty as the primary potential cause of unfairness and an approach to address it. We design a linear programming framework to find fair utility-maximizing distributions over allocations, and we show that the linear program is robust to perturbations in the estimated parameters of the uncertain merit distributions, a key property in combining the approach with machine learning techniques.

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ICLR Conference 2021 Conference Paper

One Network Fits All? Modular versus Monolithic Task Formulations in Neural Networks

Atish Agarwala
Abhimanyu Das
Brendan Juba
Rina Panigrahy
Vatsal Sharan
Xin Wang 0116
Qiuyi (Richard) Zhang

Can deep learning solve multiple, very different tasks simultaneously? We investigate how the representations of the underlying tasks affect the ability of a single neural network to learn them jointly. We present theoretical and empirical findings that a single neural network is capable of simultaneously learning multiple tasks from a combined data set, for a variety of methods for representing tasks---for example, when the distinct tasks are encoded by well-separated clusters or decision trees over some task-code attributes. Indeed, more strongly, we present a novel analysis that shows that families of simple programming-like constructs for the codes encoding the tasks are learnable by two-layer neural networks with standard training. We study more generally how the complexity of learning such combined tasks grows with the complexity of the task codes; we find that learning many tasks can be provably hard, even though the individual tasks are easy to learn. We provide empirical support for the usefulness of the learning bounds by training networks on clusters, decision trees, and SQL-style aggregation.

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ICML Conference 2020 Conference Paper

Sample Amplification: Increasing Dataset Size even when Learning is Impossible

Brian Axelrod
Shivam Garg 0001
Vatsal Sharan
Gregory Valiant

Given data drawn from an unknown distribution, D, to what extent is it possible to “amplify” this dataset and faithfully output an even larger set of samples that appear to have been drawn from D? We formalize this question as follows: an (n, m) amplification procedure takes as input n independent draws from an unknown distribution D, and outputs a set of m > n “samples” which must be indistinguishable from m samples drawn iid from D. We consider this sample amplification problem in two fundamental settings: the case where D is an arbitrary discrete distribution supported on k elements, and the case where D is a d-dimensional Gaussian with unknown mean, and fixed covariance matrix. Perhaps surprisingly, we show a valid amplification procedure exists for both of these settings, even in the regime where the size of the input dataset, n, is significantly less than what would be necessary to learn distribution D to non-trivial accuracy. We also show that our procedures are optimal up to constant factors. Beyond these results, we describe potential applications of such data amplification, and formalize a number of curious directions for future research along this vein.

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ICML Conference 2019 Conference Paper

Compressed Factorization: Fast and Accurate Low-Rank Factorization of Compressively-Sensed Data

Vatsal Sharan
Kai Sheng Tai
Peter Bailis
Gregory Valiant

What learning algorithms can be run directly on compressively-sensed data? In this work, we consider the question of accurately and efficiently computing low-rank matrix or tensor factorizations given data compressed via random projections. We examine the approach of first performing factorization in the compressed domain, and then reconstructing the original high-dimensional factors from the recovered (compressed) factors. In both the matrix and tensor settings, we establish conditions under which this natural approach will provably recover the original factors. While it is well-known that random projections preserve a number of geometric properties of a dataset, our work can be viewed as showing that they can also preserve certain solutions of non-convex, NP-Hard problems like non-negative matrix factorization. We support these theoretical results with experiments on synthetic data and demonstrate the practical applicability of compressed factorization on real-world gene expression and EEG time series datasets.

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STOC Conference 2019 Conference Paper

Memory-sample tradeoffs for linear regression with small error

Vatsal Sharan
Aaron Sidford
Gregory Valiant

We consider the problem of performing linear regression over a stream of d -dimensional examples, and show that any algorithm that uses a subquadratic amount of memory exhibits a slower rate of convergence than can be achieved without memory constraints. Specifically, consider a sequence of labeled examples ( a 1 , b 1 ), ( a 2 , b 2 )…, with a i drawn independently from a d -dimensional isotropic Gaussian, and where b i = ⟨ a i , x ⟩ + η i , for a fixed x ∈ ℝ d with || x || 2 = 1 and with independent noise η i drawn uniformly from the interval [−2 − d /5 ,2 − d /5 ]. We show that any algorithm with at most d 2 /4 bits of memory requires at least Ω( d loglog1/є) samples to approximate x to ℓ 2 error є with probability of success at least 2/3, for є sufficiently small as a function of d . In contrast, for such є, x can be recovered to error є with probability 1− o (1) with memory O ( d 2 log(1/є)) using d examples. This represents the first nontrivial lower bounds for regression with super-linear memory, and may open the door for strong memory/sample tradeoffs for continuous optimization.

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NeurIPS Conference 2019 Conference Paper

PIDForest: Anomaly Detection via Partial Identification

Parikshit Gopalan
Vatsal Sharan
Udi Wieder

We consider the problem of detecting anomalies in a large dataset. We propose a framework called Partial Identification which captures the intuition that anomalies are easy to distinguish from the overwhelming majority of points by relatively few attribute values. Formalizing this intuition, we propose a geometric anomaly measure for a point that we call PIDScore, which measures the minimum density of data points over all subcubes containing the point. We present PIDForest: a random forest based algorithm that finds anomalies based on this definition. We show that it performs favorably in comparison to several popular anomaly detection methods, across a broad range of benchmarks. PIDForest also provides a succinct explanation for why a point is labelled anomalous, by providing a set of features and ranges for them which are relatively uncommon in the dataset.

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NeurIPS Conference 2018 Conference Paper

A Spectral View of Adversarially Robust Features

Shivam Garg
Vatsal Sharan
Brian Zhang
Gregory Valiant

Given the apparent difficulty of learning models that are robust to adversarial perturbations, we propose tackling the simpler problem of developing adversarially robust features. Specifically, given a dataset and metric of interest, the goal is to return a function (or multiple functions) that 1) is robust to adversarial perturbations, and 2) has significant variation across the datapoints. We establish strong connections between adversarially robust features and a natural spectral property of the geometry of the dataset and metric of interest. This connection can be leveraged to provide both robust features, and a lower bound on the robustness of any function that has significant variance across the dataset. Finally, we provide empirical evidence that the adversarially robust features given by this spectral approach can be fruitfully leveraged to learn a robust (and accurate) model.

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NeurIPS Conference 2018 Conference Paper

Efficient Anomaly Detection via Matrix Sketching

Vatsal Sharan
Parikshit Gopalan
Udi Wieder

We consider the problem of finding anomalies in high-dimensional data using popular PCA based anomaly scores. The naive algorithms for computing these scores explicitly compute the PCA of the covariance matrix which uses space quadratic in the dimensionality of the data. We give the first streaming algorithms that use space that is linear or sublinear in the dimension. We prove general results showing that \emph{any} sketch of a matrix that satisfies a certain operator norm guarantee can be used to approximate these scores. We instantiate these results with powerful matrix sketching techniques such as Frequent Directions and random projections to derive efficient and practical algorithms for these problems, which we validate over real-world data sets. Our main technical contribution is to prove matrix perturbation inequalities for operators arising in the computation of these measures.

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STOC Conference 2018 Conference Paper

Prediction with a short memory

Vatsal Sharan
Sham M. Kakade
Percy Liang
Gregory Valiant

We consider the problem of predicting the next observation given a sequence of past observations, and consider the extent to which accurate prediction requires complex algorithms that explicitly leverage long-range dependencies. Perhaps surprisingly, our positive results show that for a broad class of sequences, there is an algorithm that predicts well on average, and bases its predictions only on the most recent few observation together with a set of simple summary statistics of the past observations. Specifically, we show that for any distribution over observations, if the mutual information between past observations and future observations is upper bounded by I , then a simple Markov model over the most recent I /є observations obtains expected KL error є—and hence ℓ 1 error √є—with respect to the optimal predictor that has access to the entire past and knows the data generating distribution. For a Hidden Markov Model with n hidden states, I is bounded by log n , a quantity that does not depend on the mixing time, and we show that the trivial prediction algorithm based on the empirical frequencies of length O (log n /є) windows of observations achieves this error, provided the length of the sequence is d Ω(log n /є) , where d is the size of the observation alphabet. We also establish that this result cannot be improved upon, even for the class of HMMs, in the following two senses: First, for HMMs with n hidden states, a window length of log n /є is information-theoretically necessary to achieve expected KL error є, or ℓ 1 error √є. Second, the d Θ(log n /є) samples required to accurately estimate the Markov model when observations are drawn from an alphabet of size d is necessary for any computationally tractable learning/prediction algorithm, assuming the hardness of strongly refuting a certain class of CSPs.

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NeurIPS Conference 2017 Conference Paper

Learning Overcomplete HMMs

Vatsal Sharan
Sham Kakade
Percy Liang
Gregory Valiant

We study the basic problem of learning overcomplete HMMs---those that have many hidden states but a small output alphabet. Despite having significant practical importance, such HMMs are poorly understood with no known positive or negative results for efficient learning. In this paper, we present several new results---both positive and negative---which help define the boundaries between the tractable-learning setting and the intractable setting. We show positive results for a large subclass of HMMs whose transition matrices are sparse, well-conditioned and have small probability mass on short cycles. We also show that learning is impossible given only a polynomial number of samples for HMMs with a small output alphabet and whose transition matrices are random regular graphs with large degree. We also discuss these results in the context of learning HMMs which can capture long-term dependencies.

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ICML Conference 2017 Conference Paper

Orthogonalized ALS: A Theoretically Principled Tensor Decomposition Algorithm for Practical Use

Vatsal Sharan
Gregory Valiant

The popular Alternating Least Squares (ALS) algorithm for tensor decomposition is efficient and easy to implement, but often converges to poor local optima—particularly when the weights of the factors are non-uniform. We propose a modification of the ALS approach that is as efficient as standard ALS, but provably recovers the true factors with random initialization under standard incoherence assumptions on the factors of the tensor. We demonstrate the significant practical superiority of our approach over traditional ALS for a variety of tasks on synthetic data—including tensor factorization on exact, noisy and over-complete tensors, as well as tensor completion—and for computing word embeddings from a third-order word tri-occurrence tensor.

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