Sihan Liu

ICML Conference 2025 Conference Paper

Batch List-Decodable Linear Regression via Higher Moments

• Ilias Diakonikolas
• Daniel M. Kane
• Sushrut Karmalkar
• Sihan Liu
• Thanasis Pittas

We study the task of list-decodable linear regression using batches, recently introduced by Das et al. 2023. . In this setting, we are given $m$ batches with each batch containing $n$ points in $\mathbb R^d$. A batch is called clean if the points it contains are i. i. d. samples from an unknown linear regression distribution. For a parameter $\alpha \in (0, 1/2)$, an unknown $\alpha$-fraction of the batches are clean and no assumptions are made on the remaining batches. The goal is to output a small list of vectors at least one of which is close to the true regressor vector in $\ell_2$-norm. Das et al. 2023 gave an efficient algorithm for this task, under natural distributional assumptions, with the following guarantee. Under the assumption that the batch size satisfies $n \geq \tilde{\Omega}(\alpha^{-1})$ and the total number of batches is $m = \text{poly}(d, n, 1/\alpha)$, their algorithm runs in polynomial time and outputs a list of $O(1/\alpha^2)$ vectors at least one of which is $\tilde{O}(\alpha^{-1/2}/\sqrt{n})$ close to the target regressor. Here we design a new polynomial-time algorithm for this task with significantly stronger guarantees under the assumption that the low-degree moments of the covariates distribution are Sum-of-Squares (SoS) certifiably bounded. Specifically, for any constant $\delta>0$, as long as the batch size is $n \geq \Omega_{\delta}(\alpha^{-\delta})$ and the degree-$\Theta(1/\delta)$ moments of the covariates are SoS certifiably bounded, our algorithm uses $m = \text{poly}((dn)^{1/\delta}, 1/\alpha)$ batches, runs in polynomial-time, and outputs an $O(1/\alpha)$-sized list of vectors one of which is $O(\alpha^{-\delta/2}/\sqrt{n})$ close to the target. That is, our algorithm substantially improves both the minimum batch size and the final error guarantee, while achieving the optimal list size. Our approach leverages higher-order moment information by carefully combining the SoS paradigm interleaved with an iterative method and a novel list pruning procedure for this setting. In the process, we give an SoS proof of the Marcinkiewicz-Zygmund inequality that may be of broader applicability.

STOC Conference 2025 Conference Paper

Entangled Mean Estimation in High Dimensions

• Ilias Diakonikolas
• Daniel M. Kane
• Sihan Liu
• Thanasis Pittas

FOCS Conference 2025 Conference Paper

PTF Testing Lower Bounds for Non-Gaussian Component Analysis

• Ilias Diakonikolas
• Daniel M. Kane
• Sihan Liu
• Thanasis Pittas

This work studies information-computation gaps for statistical problems. A common approach for providing evidence of such gaps is to show sample complexity lower bounds (that are stronger than the information-theoretic optimum) against natural models of computation. A popular such model in the literature is the family of low-degree polynomial tests. While these tests are defined in such a way that make them easy to analyze, the class of algorithms that they rule out is somewhat restricted. An important goal in this context has been to obtain lower bounds against the stronger and more natural class of low-degree Polynomial Threshold Function (PTF) tests, i. e. , any test that can be expressed as comparing some low-degree polynomial of the data to a threshold. Proving lower bounds against PTF tests has turned out to be challenging. Indeed, we are not aware of any non-trivial PTF testing lower bounds in the literature. In this paper, we establish the first non-trivial PTF testing lower bounds for a range of statistical tasks. Specifically, we prove a near-optimal PTF testing lower bound for Non-Gaussian Component Analysis (NGCA). Our NGCA lower bound implies similar lower bounds for a number of other statistical problems. Our proof leverages a connection to recent work on pseudorandom generators for PTFs and recent techniques developed in that context. At the technical level, we develop several tools of independent interest, including novel structural results for analyzing the behavior of low-degree polynomials restricted to random directions.

NeurIPS Conference 2025 Conference Paper

Replicable Distribution Testing

• Ilias Diakonikolas
• Jingyi Gao
• Daniel Kane
• Sihan Liu
• Christopher Ye

We initiate a systematic investigation of distribution testing in the framework of algorithmic replicability. Specifically, given independent samples from a collection of probability distributions, the goal is to characterize the sample complexity of replicably testing natural properties of the underlying distributions. On the algorithmic front, we develop new replicable algorithms for testing closeness and independence of discrete distributions. On the lower bound front, we develop a new methodology for proving sample complexity lower bounds for replicable testing that may be of broader interest. As an application of our technique, we establish near-optimal sample complexity lower bounds for replicable uniformity testing---answering an open question from prior work---and closeness testing.

NeurIPS Conference 2024 Conference Paper

Don't Look Twice: Faster Video Transformers with Run-Length Tokenization

• Rohan Choudhury
• Guanglei Zhu
• Sihan Liu
• Koichiro Niinuma
• Kris M. Kitani
• László A. Jeni

Video transformers are slow to train due to extremely large numbers of input tokens, even though many video tokens are repeated over time. Existing methods to remove uninformative tokens either have significant overhead, negating any speedup, or require tuning for different datasets and examples. We present Run-Length Tokenization (RLT), a simple approach to speed up video transformers inspired by run-length encoding for data compression. RLT efficiently finds and removes `runs' of patches that are repeated over time before model inference, then replaces them with a single patch and a positional encoding to represent the resulting token's new length. Our method is content-aware, requiring no tuning for different datasets, and fast, incurring negligible overhead. RLT yields a large speedup in training, reducing the wall-clock time to fine-tune a video transformer by 30% while matching baseline model performance. RLT also works without training, increasing model throughput by 35% with only 0. 1% drop in accuracy. RLT speeds up training at 30 FPS by more than 100%, and on longer video datasets, can reduce the token count by up to 80\%. Our project page is at rccchoudhury. github. io/projects/rlt.

SODA Conference 2024 Conference Paper

Online Robust Mean Estimation

• Daniel M. Kane
• Ilias Diakonikolas
• Hanshen Xiao
• Sihan Liu

FOCS Conference 2024 Conference Paper

Replicability in High Dimensional Statistics

• Max Hopkins
• Russell Impagliazzo
• Daniel M. Kane
• Sihan Liu
• Christopher Ye 0001

The replicability crisis is a major issue across nearly all areas of empirical science, calling for the formal study of replicability in statistics. Motivated in this context, [Impagliazzo, Lei, Pitassi, and Sorrell STOC 2022] introduced the notion of replicable learning algorithms, and gave basic procedures for 1-dimensional tasks including statistical queries. In this work, we study the computational and statistical cost of replicability for several fundamental high dimensional statistical tasks, including multi-hypothesis testing and mean estimation. Our main contribution establishes a computational and statistical equivalence between optimal replicable algorithms and high dimensional isoperimetric tilings. As a consequence, we obtain matching sample complexity upper and lower bounds for replicable mean estimation of distributions with bounded covariance, resolving an open problem of [Bun, Gaboardi, Hopkins, Impagliazzo, Lei, Pitassi, Sivakumar, and Sorrell, STOC 2023] and for the $N$ -Coin Problem, resolving a problem of [Karbasi, Velegkas, Yang, and Zhou, NeurIPS 2023] up to log factors. While our equivalence is computational, allowing us to shave $\log$ factors in sample complexity from the best known efficient algorithms, efficient isoperimetric tilings are not known. To circumvent this, we introduce several relaxed paradigms that do allow for sample and computationally efficient algorithms, including allowing pre-processing, adaptivity, and approximate replicability. In these cases we give efficient algorithms matching or beating the best known sample complexity for mean estimation and the coin problem, including a generic procedure that reduces the standard quadratic overhead of replicability to linear in expectation.

NeurIPS Conference 2024 Conference Paper

Replicable Uniformity Testing

• Sihan Liu
• Christopher Ye

Uniformity testing is arguably one of the most fundamental distribution testing problems. Given sample access to an unknown distribution $\mathbf{p}$ on $[n]$, one must decide if $\mathbf{p}$ is uniform or $\varepsilon$-far from uniform (in total variation distance). A long line of work established that uniformity testing has sample complexity $\Theta(\sqrt{n}\varepsilon^{-2})$. However, when the input distribution is neither uniform nor far from uniform, known algorithms may have highly non-replicable behavior. Consequently, if these algorithms are applied in scientific studies, they may lead to contradictory results that erode public trust in science. In this work, we revisit uniformity testing under the framework of algorithmic replicability [STOC '22], requiring the algorithm to be replicable under arbitrary distributions. While replicability typically incurs a $\rho^{-2}$ factor overhead in sample complexity, we obtain a replicable uniformity tester using only $\tilde{O}(\sqrt{n} \varepsilon^{-2} \rho^{-1})$ samples. To our knowledge, this is the first replicable learning algorithm with (nearly) linear dependence on $\rho$. Lastly, we consider a class of ``symmetric" algorithms [FOCS '00] whose outputs are invariant under relabeling of the domain $[n]$, which includes all existing uniformity testers (including ours). For this natural class of algorithms, we prove a nearly matching sample complexity lower bound for replicable uniformity testing.

STOC Conference 2024 Conference Paper

Super Non-singular Decompositions of Polynomials and Their Application to Robustly Learning Low-Degree PTFs

• Ilias Diakonikolas
• Daniel M. Kane
• Vasilis Kontonis
• Sihan Liu
• Nikos Zarifis

STOC Conference 2024 Conference Paper

Testing Closeness of Multivariate Distributions via Ramsey Theory

• Ilias Diakonikolas
• Daniel M. Kane
• Sihan Liu

We investigate the statistical task of closeness (or equivalence) testing for multidimensional distributions. Specifically, given sample access to two unknown distributions p , q on d , we want to distinguish between the case that p = q versus || p − q || A k > є, where || p − q || A k denotes the generalized A k distance between p and q — measuring the maximum discrepancy between the distributions over any collection of k disjoint, axis-aligned rectangles. Our main result is the first closeness tester for this problem with sub-learning sample complexity in any fixed dimension and a nearly-matching sample complexity lower bound. In more detail, we provide a computationally efficient closeness tester with sample complexity O (( k 6/7 / poly d (є)) log d ( k )). On the lower bound side, we establish a qualitatively matching sample complexity lower bound of Ω( k 6/7 / poly (є)), even for d =2. These sample complexity bounds are surprising because the sample complexity of the problem in the univariate setting is Θ( k 4/5 / poly (є)). This has the interesting consequence that the jump from one to two dimensions leads to a substantial increase in sample complexity, while increases beyond that do not. As a corollary of our general A k tester, we obtain d T V -closeness testers for pairs of k -histograms on d over a common unknown partition, and pairs of uniform distributions supported on the union of k unknown disjoint axis-aligned rectangles. Both our algorithm and our lower bound make essential use of tools from Ramsey theory.

NeurIPS Conference 2023 Conference Paper

Efficient Testable Learning of Halfspaces with Adversarial Label Noise

• Ilias Diakonikolas
• Daniel Kane
• Vasilis Kontonis
• Sihan Liu
• Nikos Zarifis

We give the first polynomial-time algorithm for the testable learning of halfspaces in the presence of adversarial label noise under the Gaussian distribution. In the recently introduced testable learning model, one is required to produce a tester-learner such that if the data passes the tester, then one can trust the output of the robust learner on the data. Our tester-learner runs in time $\text{poly}(d/\epsilon)$ and outputs a halfspace with misclassification error $O(\text{opt})+\epsilon$, where $\text{opt}$ is the 0-1 error of the best fitting halfspace. At a technical level, our algorithm employs an iterative soft localization technique enhanced with appropriate testers to ensure that the data distribution is sufficiently similar to a Gaussian. Finally, our algorithm can be readily adapted to yield an efficient and testable active learner requiring only $d ~ \text{polylog}(1/\epsilon)$ labeled examples.

SODA Conference 2023 Conference Paper

Sampling Equilibria: Fast No-Regret Learning in Structured Games

• Daniel Beaglehole
• Max Hopkins
• Daniel M. Kane
• Sihan Liu
• Shachar Lovett

Learning and equilibrium computation in games are fundamental problems across computer science and economics, with applications ranging from politics to machine learning. Much of the work in this area revolves around a simple algorithm termed randomized weighted majority (RWM), also known as “Hedge” or “Multiplicative Weights Update, ” which is well known to achieve statistically optimal rates in adversarial settings (Littlestone and Warmuth '94, Freund and Schapire '99). Unfortunately, RWM comes with an inherent computational barrier: it requires maintaining and sampling from a distribution over all possible actions. In typical settings of interest the action space is exponentially large, seemingly rendering RWM useless in practice. In this work, we refute this notion for a broad variety of structured games, showing it is possible to efficiently (approximately) sample the action space in RWM in polylogarithmic time. This gives the first efficient no-regret algorithms for problems such as the ( discrete ) Colonel Blotto game, matroid congestion, matroid security, and basic dueling games. As an immediate corollary, we give a polylogarithmic time meta-algorithm to compute approximate Nash Equilibria for these games that is exponentially faster than prior methods in several important settings. Further, our algorithm is the first to efficiently compute equilibria for more involved variants of these games with general sums, more than two players, and, for Colonel Blotto, multiple resource types. Our results also greatly generalize earlier work on efficient RWM-based techniques for exponential strategy sets from (Cesa-Bianchi and Lugosi '09).

NeurIPS Conference 2022 Conference Paper

Nearly-Tight Bounds for Testing Histogram Distributions

• Clément L Canonne
• Ilias Diakonikolas
• Daniel Kane
• Sihan Liu

We investigate the problem of testing whether a discrete probability distribution over an ordered domain is a histogram on a specified number of bins. One of the most common tools for the succinct approximation of data, $k$-histograms over $[n]$, are probability distributions that are piecewise constant over a set of $k$ intervals. Given samples from an unknown distribution $\mathbf p$ on $[n]$, we want to distinguish between the cases that $\mathbf p$ is a $k$-histogram versus far from any $k$-histogram, in total variation distance. Our main result is a sample near-optimal and computationally efficient algorithm for this testing problem, and a nearly-matching (within logarithmic factors) sample complexity lower bound, showing that the testing problem has sample complexity $\widetilde \Theta (\sqrt{nk} / \epsilon + k / \epsilon^2 + \sqrt{n} / \epsilon^2)$.