Study hypothesis testing under quantized samples with communication constraints, achieving near-optimal sample complexity.
problem Optimizing hypothesis testing with quantized samples and communication constraints.
method Developed a polynomial-time algorithm achieving near-optimal sample complexity under communication constraints.
result Achieved near-optimal sample complexity under communication constraints, with a logarithmic factor increase over unconstrained setting.
Paper resolves open problems on sample complexity in binary hypothesis testing.
problem Open problems in distributed simple binary hypothesis testing under information constraints.
method One-shot lower bound on Bayes error, streamlined sample complexity formula, reverse data-processing inequality.
result Optimally tight sample complexity bounds for communication-constrained simple binary hypothesis testing.
Optimized testing of discrete distributions using predicted data.
problem Testing discrete distributions with reduced sample complexity.
method Adaptable algorithms that use a predicted distribution to reduce sample size.
result Optimal sample complexity improvements with self-adjusting algorithms.
A simple algorithm for Gaussian mean testing with optimal sample complexity.
problem Distinguishing between standard Gaussian and other Gaussian distributions with unknown mean and covariance.
method An extremely simple algorithm with a one-page analysis.
result Optimal sample complexity of Θ(√d/ε^2) with sample linear time.
Optimal testing of discrete distributions with high probability, achieving sample complexity bounds.
problem Testing discrete distributions with high probability accuracy.
method Characterizing sample complexity as a function of parameters like δ, providing sample-optimal testers.
result Optimal algorithms for closeness and independence testing, achieving within constant factors of information-theoretic lower bounds.
New algorithms test independence with fewer samples by using predictive information.
problem Testing independence of distributions with limited samples.
method Augmented distribution testing framework that incorporates predictive information.
result Optimal sample complexity achieved, matching lower bounds.
In this work we present novel differentially private identity (goodness-of-fit) testers for natural and widely studied classes of multivariate product distributions: Gaussians in Rd with known covariance and product distributions over {±1}d. Our testers have improved sample complexity compared to …
Study improves sample complexity for distinguishing continuous distributions and causal relationships.
problem Distinguishing continuous distributions and causal relationships in the presence of unobserved confounding.
method Proposed an estimator of KL divergence based on von Mises expansion for closeness testing.
result Established sample complexity guarantees for causal discovery in non-linear models with continuous variables and unobserved confounding.
Robust test for distributions under Hellinger distance, simpler than optimal tests.
problem Testing and estimating distributions robustly under Hellinger distance.
method Simple robust hypothesis test with optimal sample complexity, robust to Hellinger distance perturbations.
result Empirically demonstrated robustness and power of the test on canonical distributions.
Formula derived for sample complexity in binary hypothesis testing.
problem Determine the minimum number of samples to distinguish between two distributions.
method Developed a formula for sample complexity in both prior-free and Bayesian settings, using Jensen-Shannon and Hellinger divergences.
result Formula characterizes sample complexity for a wide range of error parameters, up to multiplicative constants.
Meta two-sample testing uses auxiliary data to quickly find powerful tests from limited samples.
problem Challenges in identifying powerful kernels for distinguishing complex distributions with limited data.
method Introduces meta two-sample testing (M2ST) to leverage abundant auxiliary data on related tasks.
result Proposed algorithms improve over baselines and identify powerful tests from scarce observations.
Robust covariance testing requires significantly more samples in contaminated data.
problem Testing the covariance matrix of a high-dimensional Gaussian in the presence of contamination.
method We study the problem in the Huber's contamination model, distinguishing between the identity matrix and matrices far from it in Frobenius norm.
result The sample complexity of covariance testing increases dramatically to Ω(d2) in the contaminated setting. In this work, we consider the sample complexity required for testing the monotonicity of distributions over partial orders. A distribution p over a poset is monotone if, for any pair of domain elements x and y such that x⪯y, p(x)≤p(y). To understand the sample complexity of this problem, we intro…
Study shows a tradeoff between sample complexity and computational efficiency for learning halfspaces with random noise.
problem PAC learning γ-margin halfspaces with Random Classification Noise.
method Established an information-computation tradeoff and provided a simple efficient algorithm with sample complexity O(1/(γ^2 ε^2)). Also, proved lower bounds for SQ algorithms and low-degree polynomial tests.
result Inherent gap between sample complexity and computational efficiency for learning halfspaces with random noise.
New uniformity tester ensures consistent results across different samples.
problem Non-replicable behavior of uniformity testing algorithms.
method Develops a replicable uniformity tester with improved sample complexity.
result Achieves nearly linear dependence on replicability factor ρ. New algorithms estimate and test collision probability with near-optimal sample complexity.
problem Estimating and testing collision probability in discrete distributions.
method Developed algorithms for (α,β)-local differential privacy and sequential testing. result Achieved nearly optimal sample complexity for estimating and testing collision probability.
The paper designs tests for comparing ranked preference data and finds significant differences.
problem Comparing pairwise comparison and ranking data in various applications.
method Developed two-sample tests for pairwise comparison and ranking data, proving upper and lower bounds.
result Upper and lower bounds show tightness of the proposed tests, and significant differences in preferences were found.
We study distribution testing with communication and memory constraints in the following computational models: (1) The {\em one-pass streaming model} where the goal is to minimize the sample complexity of the protocol subject to a memory constraint, and (2) A {\em distributed model} where the data samples reside at mul…
Reduces identity testing of reversible Markov chains to simpler symmetric chain tests.
problem Testing identity of reversible Markov chains from a single trajectory.
method Using lumping-congruent Markov embeddings, the problem is simplified to testing symmetric chains over a larger state space.
result Achieves state-of-the-art sample complexity for identity testing.
Paper tests DPPs for diversity models, distinguishing them from other distributions.
problem Testing whether a given distribution is a Determinantal Point Process (DPP) or far from any DPP.
method Proposes the first algorithm for DPP testing and establishes a lower bound on sample complexity.
result Establishes a matching lower bound on the sample complexity of DPP testing.
Hypothesis testing plays a central role in statistical inference, and is used in many settings where privacy concerns are paramount. This work answers a basic question about privately testing simple hypotheses: given two distributions P and Q, and a privacy level ε, how many i.i.d. samples are needed to…
Study sample complexity of robust binary hypothesis testing under different contamination models.
problem Analyzing the sample complexity of robust binary hypothesis testing under various contamination models.
method Examined three standard contamination models: ε-additive (Huber), ε-subtractive, and ε-total variation (TV). Provided explicit formulas for least favourable distributions and compared sample complexities across models.
result Sample complexities are highly unstable in the contamination parameter ε and comparable up to constant-factor rescaling of ε across models.
Cer-Eval saves LLM evaluation costs while maintaining accuracy.
problem Challenges in evaluating large language models due to large dataset requirements.
method Adapts to different evaluation objectives, uses test sample complexity, and develops a partition-based algorithm.
result Cer-Eval can save 20-40% test points with comparable accuracy and 95% confidence guarantee.
The study examines property testing and estimation under non-identically distributed samples, finding necessary and sufficient sample complexities.
problem Property testing and estimation under non-identically distributed samples.
method Analysis of distributional property testing and estimation in settings with heterogeneous entities.
result Necessary and sufficient sample complexities for property testing and estimation under non-identically distributed samples.
A test for comparing networks using stochastic block models.
problem Determining if two network datasets come from the same model.
method Adopting stochastic block models, the study introduces an efficient algorithm to match estimated network parameters and develops a powerful test.
result The test is consistent and asymptotically follows a chi-squared distribution.
A new CVaR test reduces group performance disparity detection complexity.
problem Detecting performance disparities across multiple sensitive groups in ML models.
method Conditional Value-at-Risk (CVaR) testing to reduce sample complexity.
result Sample complexity reduced exponentially to be at most the square root of the number of groups.
Two statistical tasks are shown to have equivalent sample complexity.
problem Determining if a function depends on only a few variables and identifying those variables.
method Proved statistical equivalence of feature selection and junta testing through sample complexity analysis.
result Brute-force algorithm is sample-optimal for both tasks with optimal sample size.
We study the problem of hypothesis testing between two discrete distributions, where we only have access to samples after the action of a known reversible Markov chain, playing the role of noise. We derive instance-dependent minimax rates for the sample complexity of this problem, and show how its dependence in time is…
New insights into distribution testing with tolerance.
problem Tolerant distribution testing in the intermediate regime.
method Characterization of sample complexity as a function of n, ε1, and ε2. result Smooth tradeoff between sample complexity and the ratio ε1/ε22. A new method optimizes MMD test power by dynamically selecting kernels, overcoming traditional trade-offs.
problem Fixed kernels fail to distinguish certain distributions, leading to overfitting and variance collapse.
method Complexity-Penalized MMD (CP-MMD) criterion, derived from concentration inequality, optimizes kernel selection.
result CP-MMD maximizes true test power while ensuring unconditional Type-I validity, matching or exceeding state-of-the-art performance.
The paper develops a new method to test if two multidimensional distributions are equivalent or significantly different.
problem Testing equivalence of multidimensional distributions with sub-linear sample complexity.
method Uses generalized A_k distance and Ramsey theory to develop a computationally efficient closeness tester.
result First sub-linear sample complexity closeness tester for multidimensional distributions.
The paper analyzes a neural network two-sample test using kernel analysis.
problem Determining if two datasets come from the same distribution.
method Time-analysis on a neural tangent kernel (NTK) two-sample test, extending to realistic neural network dynamics.
result Training times needed to detect deviations are well-separated in null and alternative hypothesis scenarios.
This work explores test-time scaling strategies for LLMs, improving sample efficiency and expressiveness.
problem Understanding the sample efficiency and expressiveness of test-time scaling strategies for LLMs.
method Established separation and expressiveness results for self-consistency, best-of-n, and self-correction strategies. result Self-correction enables Transformers to simulate online learning over multiple tasks without prior knowledge.
Improved MMD test for two-sample testing with random Fourier features.
problem Quadratic-time complexity of MMD test for large-scale analysis.
method Approximated MMD test using random Fourier features, investigating time-power trade-off.
result Sub-quadratic time complexity with same minimax separation rates as MMD test.
Deep neural nets optimize kernel parameters for non-parametric two-sample tests.
problem Determining if two samples come from the same distribution.
method Deep kernels trained to maximize test power, adapting to distribution smoothness and shape.
result Deep kernels outperform simpler kernels in high dimensions and complex data.
There has been significant study on the sample complexity of testing properties of distributions over large domains. For many properties, it is known that the sample complexity can be substantially smaller than the domain size. For example, over a domain of size n, distinguishing the uniform distribution from distrib…
Kernel two-sample testing is a useful statistical tool in determining whether data samples arise from different distributions without imposing any parametric assumptions on those distributions. However, raw data samples can expose sensitive information about individuals who participate in scientific studies, which make…
An algorithm solves optimization problems with large sample sets, improving worst-case complexity.
problem Continuous nonlinear-equality-constrained optimization problems with large numbers of terms.
method Progressively sampled finite sets to solve related problems with growing sample sizes.
result Better worst-case sample complexity compared to solving with full sets of samples.
Study binary hypothesis testing with privacy and communication constraints.
problem Binary hypothesis testing under local differential privacy and communication constraints.
method Qualifies results as minimax or instance optimal, develops instance-optimal algorithms.
result Achieves minimum possible sample complexity under both privacy and communication constraints.
Study clusters distributions with known or unknown clusters using distribution testing.
problem Cluster distributions that are ε-far in total variation. method Distribution testing approach to establish upper and lower bounds on sample complexity.
result Achieves tight sample complexity bounds for all regimes (up to a logarithmic factor).
Paper extends Chernoff sampling for active testing and parameter estimation, improving neural network and regression models.
problem Reducing sample complexity in hypothesis testing and model parameter estimation.
method Developed an extension of Chernoff sampling for active learning and parameter estimation.
result Non-asymptotic bounds for sample complexity and estimation error in active learning.
Improved SV estimator for efficient data valuation.
problem Computational inefficiency in Shapley value estimation.
method Group Testing-based SV estimator with improvements.
result Enhanced asymptotic sample complexity and insights into challenges.
Study tests if a probability measure is near a real algebraic variety.
problem Deciding if a probability measure is near a real algebraic variety.
method Proved upper bound on sample complexity, reduced to semialgebraic decision problem, studied Hausdorff geometry of real algebraic varieties.
result Upper bound on sample complexity for testing variety hypothesis.
New sampling and identity-testing methods for mixtures of distributions that don't satisfy approximate tensorization of entropy.
problem Sampling and identity-testing for mixtures of distributions that don't satisfy approximate tensorization of entropy.
method Fast mixing of Glauber dynamics and efficient identity-testers in the coordinate-conditional sampling access model.
result Efficient identity-testers for mixtures of ATE distributions in the coordinate-conditional sampling access model.
DP-SPRT improves privacy in sequential tests with near-optimal error rates.
problem Privacy constraints in sequential probability ratio tests.
method A wrapper for SPRT that uses a private mechanism to determine when to stop based on predefined intervals.
result DP-SPRT achieves near-optimal error rates and privacy guarantees.
Learning capacity measures model complexity, correlating with test loss and sample size.
problem Understanding model complexity and its relation to test performance.
method Formal correspondence between thermodynamics and inference; learning capacity as a measure of effective dimensionality.
result Learning capacity correlates with test loss and is a small fraction of model parameters.
We study three fundamental statistical-learning problems: distribution estimation, property estimation, and property testing. We establish the profile maximum likelihood (PML) estimator as the first unified sample-optimal approach to a wide range of learning tasks. In particular, for every alphabet size k and desired…
New test detects independence in streaming data, adapting to data complexity.
problem Independence testing in streaming data with adaptive stopping.
method Sequential kernelized independence tests using betting principles.
result Valid inference in streaming data with improved power.