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Jerry Li

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19 papers

2 author rows

NeurIPS Conference 2025 Conference Paper

Robust Estimation Under Heterogeneous Corruption Rates

Syomantak Chaudhuri
Jerry Li
Thomas Courtade

We study the problem of robust estimation under heterogeneous corruption rates, where each sample may be independently corrupted with a known but non-identical probability. This setting arises naturally in distributed and federated learning, crowdsourcing, and sensor networks, yet existing robust estimators typically assume uniform or worst-case corruption, ignoring structural heterogeneity. For mean estimation for multivariate bounded distributions and univariate gaussian distributions, we give tight minimax rates for all heterogeneous corruption patterns. For multivariate gaussian mean estimation and linear regression, we establish the minimax rate for squared error up to a factor of $\sqrt{d}$, where $d$ is the dimension. Roughly, our findings suggest that samples beyond a certain corruption threshold may be discarded by the optimal estimators -- this threshold is determined by the empirical distribution of the corruption rates given.

ICLR Conference 2024 Conference Paper

KITAB: Evaluating LLMs on Constraint Satisfaction for Information Retrieval

Marah I Abdin
Suriya Gunasekar
Varun Chandrasekaran
Jerry Li
Mert Yüksekgönül
Rahee Ghosh Peshawaria
Ranjita Naik
Besmira Nushi

We study the ability of state-of-the art models to answer constraint satisfaction queries for information retrieval (e.g., “a list of ice cream shops in San Diego”). In the past, such queries were considered as tasks that could only be solved via web-search or knowledge bases. More recently, large language models (LLMs) have demonstrated initial emergent abilities in this task. However, many current retrieval benchmarks are either saturated or do not measure constraint satisfaction. Motivated by rising concerns around factual incorrectness and hallucinations of LLMs, we present KITAB, a new dataset for measuring constraint satisfaction abilities of language models. KITAB consists of book-related data across more than 600 authors and 13,000 queries, and also offers an associated dynamic data collection and constraint verification approach for acquiring similar test data for other authors. Our extended experiments on GPT4 and GPT3.5 characterize and decouple common failure modes across dimensions such as information popularity, constraint types, and context availability. Results show that in the absence of context, models exhibit severe limitations as measured by irrelevant information, factual errors, and incompleteness, many of which exacerbate as information popularity decreases. While context availability mitigates irrelevant information, it is not helpful for satisfying constraints, identifying fundamental barriers to constraint satisfaction. We open source our contributions to foster further research on improving constraint satisfaction abilities of future models.

NeurIPS Conference 2024 Conference Paper

Semi-Random Matrix Completion via Flow-Based Adaptive Reweighting

Jonathan A. Kelner
Jerry Li
Allen Liu
Aaron Sidford
Kevin Tian

We consider the well-studied problem of completing a rank-$r$, $\mu$-incoherent matrix $\mathbf{M} \in \mathbb{R}^{d \times d}$ from incomplete observations. We focus on this problem in the semi-random setting where each entry is independently revealed with probability at least $p = \frac{\textup{poly}(r, \mu, \log d)}{d}$. Whereas multiple nearly-linear time algorithms have been established in the more specialized fully-random setting where each entry is revealed with probablity exactly $p$, the only known nearly-linear time algorithm in the semi-random setting is due to [CG18], whose sample complexity has a polynomial dependence on the inverse accuracy and condition number and thus cannot achieve high-accuracy recovery. Our main result is the first high-accuracy nearly-linear time algorithm for solving semi-random matrix completion, and an extension to the noisy observation setting. Our result builds upon the recent short-flat decomposition framework of [KLLST23a, KLLST23b] and leverages fast algorithms for flow problems on graphs to solve adaptive reweighting subproblems efficiently.

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NeurIPS Conference 2023 Conference Paper

Structured Semidefinite Programming for Recovering Structured Preconditioners

Arun Jambulapati
Jerry Li
Christopher Musco
Kirankumar Shiragur
Aaron Sidford
Kevin Tian

We develop a general framework for finding approximately-optimal preconditioners for solving linear systems. Leveraging this framework we obtain improved runtimes for fundamental preconditioning and linear system solving problems including: Diagonal preconditioning. We give an algorithm which, given positive definite $\mathbf{K} \in \mathbb{R}^{d \times d}$ with $\mathrm{nnz}(\mathbf{K})$ nonzero entries, computes an $\epsilon$-optimal diagonal preconditioner in time $\widetilde{O}(\mathrm{nnz}(\mathbf{K}) \cdot \mathrm{poly}(\kappa^\star, \epsilon^{-1}))$, where $\kappa^\star$ is the optimal condition number of the rescaled matrix. Structured linear systems. We give an algorithm which, given $\mathbf{M} \in \mathbb{R}^{d \times d}$ that is either the pseudoinverse of a graph Laplacian matrix or a constant spectral approximation of one, solves linear systems in $\mathbf{M}$ in $\widetilde{O}(d^2)$ time. Our diagonal preconditioning results improve state-of-the-art runtimes of $\Omega(d^{3. 5})$ attained by general-purpose semidefinite programming, and our solvers improve state-of-the-art runtimes of $\Omega(d^{\omega})$ where $\omega > 2. 3$ is the current matrix multiplication constant. We attain our results via new algorithms for a class of semidefinite programs (SDPs) we call matrix-dictionary approximation SDPs, which we leverage to solve an associated problem we call matrix-dictionary recovery.

NeurIPS Conference 2022 Conference Paper

Learning (Very) Simple Generative Models Is Hard

Sitan Chen
Jerry Li
Yuanzhi Li

Motivated by the recent empirical successes of deep generative models, we study the computational complexity of the following unsupervised learning problem. For an unknown neural network $F: \mathbb{R}^d\to\mathbb{R}^{d'}$, let $D$ be the distribution over $\mathbb{R}^{d'}$ given by pushing the standard Gaussian $\mathcal{N}(0, \textrm{Id}_d)$ through $F$. Given i. i. d. samples from $D$, the goal is to output *any* distribution close to $D$ in statistical distance. We show under the statistical query (SQ) model that no polynomial-time algorithm can solve this problem even when the output coordinates of $F$ are one-hidden-layer ReLU networks with $\log(d)$ neurons. Previously, the best lower bounds for this problem simply followed from lower bounds for *supervised learning* and required at least two hidden layers and $\textrm{poly}(d)$ neurons [Daniely-Vardi '21, Chen-Gollakota-Klivans-Meka '22]. The key ingredient in our proof is an ODE-based construction of a compactly supported, piecewise-linear function $f$ with polynomially-bounded slopes such that the pushforward of $\mathcal{N}(0, 1)$ under $f$ matches all low-degree moments of $\mathcal{N}(0, 1)$.

NeurIPS Conference 2022 Conference Paper

Robust Model Selection and Nearly-Proper Learning for GMMs

Allen Liu
Jerry Li
Ankur Moitra

In learning theory, a standard assumption is that the data is generated from a finite mixture model. But what happens when the number of components is not known in advance? The problem of estimating the number of components, also called model selection, is important in its own right but there are essentially no known efficient algorithms with provable guarantees. In this work, we study the problem of model selection for univariate Gaussian mixture models (GMMs). Given $\textsf{poly}(k/\epsilon)$ samples from a distribution that is $\epsilon$-close in TV distance to a GMM with $k$ components, we can construct a GMM with $\widetilde{O}(k)$ components that approximates the distribution to within $\widetilde{O}(\epsilon)$ in $\textsf{poly}(k/\epsilon)$ time. Thus we are able to approximately determine the minimum number of components needed to fit the distribution within a logarithmic factor. Moreover, by adapting the techniques we obtain similar results for reconstructing Fourier-sparse signals. Prior to our work, the only known algorithms for learning arbitrary univariate GMMs either output significantly more than $k$ components (e. g. $k/\epsilon^2$ components for kernel density estimates) or run in time exponential in $k$.

NeurIPS Conference 2021 Conference Paper

List-Decodable Mean Estimation in Nearly-PCA Time

Ilias Diakonikolas
Daniel Kane
Daniel Kongsgaard
Jerry Li
Kevin Tian

Robust statistics has traditionally focused on designing estimators tolerant to a minority of contaminated data. {\em List-decodable learning}~\cite{CharikarSV17} studies the more challenging regime where only a minority $\tfrac 1 k$ fraction of the dataset, $k \geq 2$, is drawn from the distribution of interest, and no assumptions are made on the remaining data. We study the fundamental task of list-decodable mean estimation in high dimensions. Our main result is a new algorithm for bounded covariance distributions with optimal sample complexity and near-optimal error guarantee, running in {\em nearly-PCA time}. Assuming the ground truth distribution on $\mathbb{R}^d$ has identity-bounded covariance, our algorithm outputs $O(k)$ candidate means, one of which is within distance $O(\sqrt{k\log k})$ from the truth. Our algorithm runs in time $\widetilde{O}(ndk)$, where $n$ is the dataset size. This runtime nearly matches the cost of performing $k$-PCA on the data, a natural bottleneck of known algorithms for (very) special cases of our problem, such as clustering well-separated mixtures. Prior to our work, the fastest runtimes were $\widetilde{O}(n^2 d k^2)$~\cite{DiakonikolasKK20}, and $\widetilde{O}(nd k^C)$ \cite{CherapanamjeriMY20} for an unspecified constant $C \geq 6$. Our approach builds on a novel soft downweighting method we term SIFT, arguably the simplest known polynomial-time mean estimator in the list-decodable setting. To develop our fast algorithms, we boost the computational cost of SIFT via a careful ``win-win-win'' analysis of an approximate Ky Fan matrix multiplicative weights procedure we develop, which may be of independent interest.

NeurIPS Conference 2021 Conference Paper

Robust Regression Revisited: Acceleration and Improved Estimation Rates

Arun Jambulapati
Jerry Li
Tselil Schramm
Kevin Tian

We study fast algorithms for statistical regression problems under the strong contamination model, where the goal is to approximately optimize a generalized linear model (GLM) given adversarially corrupted samples. Prior works in this line of research were based on the \emph{robust gradient descent} framework of \cite{PrasadSBR20}, a first-order method using biased gradient queries, or the \emph{Sever} framework of \cite{DiakonikolasKK019}, an iterative outlier-removal method calling a stationary point finder. We present nearly-linear time algorithms for robust regression problems with improved runtime or estimation guarantees compared to the state-of-the-art. For the general case of smooth GLMs (e. g. \ logistic regression), we show that the robust gradient descent framework of \cite{PrasadSBR20} can be \emph{accelerated}, and show our algorithm extends to optimizing the Moreau envelopes of Lipschitz GLMs (e. g. \ support vector machines), answering several open questions in the literature. For the well-studied case of robust linear regression, we present an alternative approach obtaining improved estimation rates over prior nearly-linear time algorithms. Interestingly, our algorithm starts with an identifiability proof introduced in the context of the sum-of-squares algorithm of \cite{BakshiP21}, which achieved optimal error rates while requiring large polynomial runtime and sample complexity. We reinterpret their proof within the Sever framework and obtain a dramatically faster and more sample-efficient algorithm under fewer distributional assumptions.

NeurIPS Conference 2020 Conference Paper

Learning Structured Distributions From Untrusted Batches: Faster and Simpler

Sitan Chen
Jerry Li
Ankur Moitra

We revisit the problem of learning from untrusted batches introduced by Qiao and Valiant [QV17]. Recently, Jain and Orlitsky [JO19] gave a simple semidefinite programming approach based on the cut-norm that achieves essentially information-theoretically optimal error in polynomial time. Concurrently, Chen et al. [CLM19] considered a variant of the problem where μ is assumed to be structured, e. g. log-concave, monotone hazard rate, t-modal, etc. In this case, it is possible to achieve the same error with sample complexity sublinear in n, and they exhibited a quasi-polynomial time algorithm for doing so using Haar wavelets. In this paper, we find an appealing way to synthesize the techniques of [JO19] and [CLM19] to give the best of both worlds: an algorithm which runs in polynomial time and can exploit structure in the underlying distribution to achieve sublinear sample complexity. Along the way, we simplify the approach of [JO19] by avoiding the need for SDP rounding and giving a more direct interpretation of it through the lens of soft filtering, a powerful recent technique in high-dimensional robust estimation. We validate the usefulness of our algorithms in preliminary experimental evaluations.

NeurIPS Conference 2020 Conference Paper

RL Unplugged: A Suite of Benchmarks for Offline Reinforcement Learning

Caglar Gulcehre
Ziyu Wang
Alexander Novikov
Thomas Paine
Sergio Gómez
Konrad Zolna
Rishabh Agarwal
Josh S. Merel

Offline methods for reinforcement learning have a potential to help bridge the gap between reinforcement learning research and real-world applications. They make it possible to learn policies from offline datasets, thus overcoming concerns associated with online data collection in the real-world, including cost, safety, or ethical concerns. In this paper, we propose a benchmark called RL Unplugged to evaluate and compare offline RL methods. RL Unplugged includes data from a diverse range of domains including games e. g. , Atari benchmark) and simulated motor control problems (e. g. , DM Control Suite). The datasets include domains that are partially or fully observable, use continuous or discrete actions, and have stochastic vs. deterministic dynamics. We propose detailed evaluation protocols for each domain in RL Unplugged and provide an extensive analysis of supervised learning and offline RL methods using these protocols. We will release data for all our tasks and open-source all algorithms presented in this paper. We hope that our suite of benchmarks will increase the reproducibility of experiments and make it possible to study challenging tasks with a limited computational budget, thus making RL research both more systematic and more accessible across the community. Moving forward, we view RL Unplugged as a living benchmark suite that will evolve and grow with datasets contributed by the research community and ourselves. Our project page is available on github.

NeurIPS Conference 2020 Conference Paper

Robust and Heavy-Tailed Mean Estimation Made Simple, via Regret Minimization

Sam Hopkins
Jerry Li
Fred Zhang

We study the problem of estimating the mean of a distribution in high dimensions when either the samples are adversarially corrupted or the distribution is heavy-tailed. Recent developments in robust statistics have established efficient and (near) optimal procedures for both settings. However, the algorithms developed on each side tend to be sophisticated and do not directly transfer to the other, with many of them having ad-hoc or complicated analyses. In this paper, we provide a meta-problem and a duality theorem that lead to a new unified view on robust and heavy-tailed mean estimation in high dimensions. We show that the meta-problem can be solved either by a variant of the Filter algorithm from the recent literature on robust estimation or by the quantum entropy scoring scheme (QUE), due to Dong, Hopkins and Li (NeurIPS '19). By leveraging our duality theorem, these results translate into simple and efficient algorithms for both robust and heavy-tailed settings. Furthermore, the QUE-based procedure has run-time that matches the fastest known algorithms on both fronts. Our analysis of Filter is through the classic regret bound of the multiplicative weights update method. This connection allows us to avoid the technical complications in previous works and improve upon the run-time analysis of a gradient-descent-based algorithm for robust mean estimation by Cheng, Diakonikolas, Ge and Soltanolkotabi (ICML '20).

NeurIPS Conference 2020 Conference Paper

Robust Gaussian Covariance Estimation in Nearly-Matrix Multiplication Time

Jerry Li
Guanghao Ye

Robust covariance estimation is the following, well-studied problem in high dimensional statistics: given $N$ samples from a $d$-dimensional Gaussian $\mathcal{N}(\boldsymbol{0}, \Sigma)$, but where an $\varepsilon$-fraction of the samples have been arbitrarily corrupted, output $\widehat{\Sigma}$ minimizing the total variation distance between $\mathcal{N}(\boldsymbol{0}, \Sigma)$ and $\mathcal{N}(\boldsymbol{0}, \widehat{\Sigma})$. This corresponds to learning $\Sigma$ in a natural affine-invariant variant of the Frobenius norm known as the \emph{Mahalanobis norm}. Previous work of Cheng et al demonstrated an algorithm that, given $N = \widetilde{\Omega}(d^2 / \varepsilon^2)$ samples, achieved a near-optimal error of $O(\varepsilon \log 1 / \varepsilon)$, and moreover, their algorithm ran in time $\widetilde{O}(T(N, d) \log \kappa / \mathrm{poly} (\varepsilon))$, where $T(N, d)$ is the time it takes to multiply a $d \times N$ matrix by its transpose, and $\kappa$ is the condition number of $\Sigma$. When $\varepsilon$ is relatively small, their polynomial dependence on $1/\varepsilon$ in the runtime is prohibitively large. In this paper, we demonstrate a novel algorithm that achieves the same statistical guarantees, but which runs in time $\widetilde{O} (T(N, d) \log \kappa)$. In particular, our runtime has no dependence on $\varepsilon$. When $\Sigma$ is reasonably conditioned, our runtime matches that of the fastest algorithm for covariance estimation without outliers, up to poly-logarithmic factors, showing that we can get robustness essentially ``for free. ''

NeurIPS Conference 2020 Conference Paper

Robust Sub-Gaussian Principal Component Analysis and Width-Independent Schatten Packing

Arun Jambulapati
Jerry Li
Kevin Tian

We develop two methods for the following fundamental statistical task: given an $\eps$-corrupted set of $n$ samples from a $d$-dimensional sub-Gaussian distribution, return an approximate top eigenvector of the covariance matrix. Our first robust PCA algorithm runs in polynomial time, returns a $1 - O(\eps\log\eps^{-1})$-approximate top eigenvector, and is based on a simple iterative filtering approach. Our second, which attains a slightly worse approximation factor, runs in nearly-linear time and sample complexity under a mild spectral gap assumption. These are the first polynomial-time algorithms yielding non-trivial information about the covariance of a corrupted sub-Gaussian distribution without requiring additional algebraic structure of moments. As a key technical tool, we develop the first width-independent solvers for Schatten-$p$ norm packing semidefinite programs, giving a $(1 + \eps)$-approximate solution in $O(p\log(\tfrac{nd}{\eps})\eps^{-1})$ input-sparsity time iterations (where $n$, $d$ are problem dimensions).

NeurIPS Conference 2019 Conference Paper

Provably Robust Deep Learning via Adversarially Trained Smoothed Classifiers

Hadi Salman
Jerry Li
Ilya Razenshteyn
Pengchuan Zhang
Huan ZHang
Sebastien Bubeck
Greg Yang

Recent works have shown the effectiveness of randomized smoothing as a scalable technique for building neural network-based classifiers that are provably robust to $\ell_2$-norm adversarial perturbations. In this paper, we employ adversarial training to improve the performance of randomized smoothing. We design an adapted attack for smoothed classifiers, and we show how this attack can be used in an adversarial training setting to boost the provable robustness of smoothed classifiers. We demonstrate through extensive experimentation that our method consistently outperforms all existing provably $\ell_2$-robust classifiers by a significant margin on ImageNet and CIFAR-10, establishing the state-of-the-art for provable $\ell_2$-defenses. Moreover, we find that pre-training and semi-supervised learning boost adversarially trained smoothed classifiers even further. Our code and trained models are available at http: //github. com/Hadisalman/smoothing-adversarial.

NeurIPS Conference 2019 Conference Paper

Quantum Entropy Scoring for Fast Robust Mean Estimation and Improved Outlier Detection

Yihe Dong
Samuel Hopkins
Jerry Li

We study two problems in high-dimensional robust statistics: \emph{robust mean estimation} and \emph{outlier detection}. In robust mean estimation the goal is to estimate the mean $\mu$ of a distribution on $\mathbb{R}^d$ given $n$ independent samples, an $\epsilon$-fraction of which have been corrupted by a malicious adversary. In outlier detection the goal is to assign an \emph{outlier score} to each element of a data set such that elements more likely to be outliers are assigned higher scores. Our algorithms for both problems are based on a new outlier scoring method we call QUE-scoring based on \emph{quantum entropy regularization}. For robust mean estimation, this yields the first algorithm with optimal error rates and nearly-linear running time $\tilde{O}(nd)$ in all parameters, improving on the previous fastest running time $\tilde{O}(\min(nd/\e^6, nd^2))$. For outlier detection, we evaluate the performance of QUE-scoring via extensive experiments on synthetic and real data, and demonstrate that it often performs better than previously proposed algorithms.

NeurIPS Conference 2018 Conference Paper

Byzantine Stochastic Gradient Descent

Dan Alistarh
Zeyuan Allen-Zhu
Jerry Li

This paper studies the problem of distributed stochastic optimization in an adversarial setting where, out of $m$ machines which allegedly compute stochastic gradients every iteration, an $\alpha$-fraction are Byzantine, and may behave adversarially. Our main result is a variant of stochastic gradient descent (SGD) which finds $\varepsilon$-approximate minimizers of convex functions in $T = \tilde{O}\big( \frac{1}{\varepsilon^2 m} + \frac{\alpha^2}{\varepsilon^2} \big)$ iterations. In contrast, traditional mini-batch SGD needs $T = O\big( \frac{1}{\varepsilon^2 m} \big)$ iterations, but cannot tolerate Byzantine failures. Further, we provide a lower bound showing that, up to logarithmic factors, our algorithm is information-theoretically optimal both in terms of sample complexity and time complexity.

NeurIPS Conference 2018 Conference Paper

Spectral Signatures in Backdoor Attacks

Brandon Tran
Jerry Li
Aleksander Madry

A recent line of work has uncovered a new form of data poisoning: so-called backdoor attacks. These attacks are particularly dangerous because they do not affect a network's behavior on typical, benign data. Rather, the network only deviates from its expected output when triggered by an adversary's planted perturbation. In this paper, we identify a new property of all known backdoor attacks, which we call spectral signatures. This property allows us to utilize tools from robust statistics to thwart the attacks. We demonstrate the efficacy of these signatures in detecting and removing poisoned examples on real image sets and state of the art neural network architectures. We believe that understanding spectral signatures is a crucial first step towards a principled understanding of backdoor attacks.

NeurIPS Conference 2017 Conference Paper

Communication-Efficient Distributed Learning of Discrete Distributions

Ilias Diakonikolas
Elena Grigorescu
Jerry Li
Abhiram Natarajan
Krzysztof Onak
Ludwig Schmidt

We initiate a systematic investigation of distribution learning (density estimation) when the data is distributed across multiple servers. The servers must communicate with a referee and the goal is to estimate the underlying distribution with as few bits of communication as possible. We focus on non-parametric density estimation of discrete distributions with respect to the l1 and l2 norms. We provide the first non-trivial upper and lower bounds on the communication complexity of this basic estimation task in various settings of interest. Specifically, our results include the following: 1. When the unknown discrete distribution is unstructured and each server has only one sample, we show that any blackboard protocol (i. e. , any protocol in which servers interact arbitrarily using public messages) that learns the distribution must essentially communicate the entire sample. 2. For the case of structured distributions, such as k-histograms and monotone distributions, we design distributed learning algorithms that achieve significantly better communication guarantees than the naive ones, and obtain tight upper and lower bounds in several regimes. Our distributed learning algorithms run in near-linear time and are robust to model misspecification. Our results provide insights on the interplay between structure and communication efficiency for a range of fundamental distribution estimation tasks.

NeurIPS Conference 2017 Conference Paper

QSGD: Communication-Efficient SGD via Gradient Quantization and Encoding

Dan Alistarh
Demjan Grubic
Jerry Li
Ryota Tomioka
Milan Vojnovic

Parallel implementations of stochastic gradient descent (SGD) have received significant research attention, thanks to its excellent scalability properties. A fundamental barrier when parallelizing SGD is the high bandwidth cost of communicating gradient updates between nodes; consequently, several lossy compresion heuristics have been proposed, by which nodes only communicate quantized gradients. Although effective in practice, these heuristics do not always guarantee convergence, and it is not clear whether they can be improved. In this paper, we propose Quantized SGD (QSGD), a family of compression schemes for gradient updates which provides convergence guarantees. QSGD allows the user to smoothly trade off \emph{communication bandwidth} and \emph{convergence time}: nodes can adjust the number of bits sent per iteration, at the cost of possibly higher variance. We show that this trade-off is inherent, in the sense that improving it past some threshold would violate information-theoretic lower bounds. QSGD guarantees convergence for convex and non-convex objectives, under asynchrony, and can be extended to stochastic variance-reduced techniques. When applied to training deep neural networks for image classification and automated speech recognition, QSGD leads to significant reductions in end-to-end training time. For example, on 16GPUs, we can train the ResNet152 network to full accuracy on ImageNet 1. 8x faster than the full-precision variant.