Paper develops online statistical inference methods for stochastic optimization using Kiefer-Wolfowitz algorithms.
problem Online statistical inference of model parameters in stochastic optimization problems.
method Kiefer-Wolfowitz algorithm with random search directions, asymptotic distribution analysis.
result Developed valid confidence intervals for online statistical inference.
New flexible confidence sequences for robust statistical inference.
problem Creating robust statistical inference methods that work under mild assumptions.
method Proposed a new class of asymptotic time-uniform confidence sequences.
result Sharp asymptotic time-uniform confidence sequences achieved under mild assumptions.
Improved estimator reduces bias in statistical learning models.
problem Asymptotic bias in classic WDRO estimator.
method Adjusted Wasserstein distributionally robust estimator.
result Asymptotic unbiased estimator with smaller MSE.
The purpose of this paper is to provide a sharp analysis on the asymptotic behavior of the Durbin-Watson statistic. We focus our attention on the first-order autoregressive process where the driven noise is also given by a first-order autoregressive process. We establish the almost sure convergence and the asymptotic n…
We analyze SGAs for statistical inference via asymptotics, improving tuning methods.
problem Improper tuning of SGAs for optimization and sampling.
method Characterize large-sample asymptotics of SGAs via step-size and sample-size scaling limits.
result Iterate averaging with large step size is robust and asymptotically has covariance proportional to MLE's.
Extends JKO scheme for iterative algorithms with unknown parameters.
problem Computational and statistical analysis of iterative algorithms with unknown parameters.
method Develops statistical methods to estimate unknown parameters and adapts JKO scheme.
result Establishes asymptotic theory for the statistical JKO scheme.
The paper analyzes Karcher means on restricted PSD matrices with statistical guarantees.
problem Statistical analysis of non-linear manifolds in machine learning.
method Intrinsic mean model on restricted PSD matrices, Karcher mean analysis, extrinsic signal-plus-noise model.
result Non-asymptotic statistical analysis of Karcher means with deterministic error bounds.
Study GLS estimator properties in multivariate regression with heteroskedastic and autocorrelated errors.
problem Asymptotic properties of GLS estimator in multivariate regression with specific error structures.
method Derive Wald statistics for linear restrictions and assess their performance.
result Wald statistics remain robust to heteroskedasticity and autocorrelation.
Study on statistical inference for nonlinear stochastic approximation with Markovian data.
problem Statistical inference for nonlinear stochastic approximation algorithms with Markovian data.
method Established a functional central limit theorem for the partial-sum process of the target parameter estimate, providing asymptotic pivotal statistics for constructing confidence intervals.
result Valid and efficient asymptotic inference method for nonlinear stochastic approximation algorithms with Markovian data.
Study improves BN TTA under distribution shift using higher-order asymptotics.
problem Improving BN TTA for changing data distributions.
method Integrates Edgeworth expansion and saddlepoint approximation with one-step M-estimation.
result Derives optimal weighting parameter for minimized mean-squared error.
Paper explores weighted averaging schemes for SGD, achieving asymptotic normality and optimality.
problem Improving convergence of SGD in various settings.
method Develops a general weighted averaging scheme for SGD and establishes asymptotic normality.
result Establishes asymptotic normality and optimality of weighted averaged SGD solutions.
The paper analyzes the statistical properties of GANs using f-divergence.
problem Understanding the statistical behavior of GANs and comparing different f-divergences. method Asymptotic analysis of f-divergence GANs, including Kullback-Leibler divergence. result Asymptotically equivalent GANs with the same discriminator classes for correctly specified models.
This paper investigates asymptotic behaviors of gradient descent algorithms (particularly accelerated gradient descent and stochastic gradient descent) in the context of stochastic optimization arising in statistics and machine learning where objective functions are estimated from available data. We show that these alg…
New test for conditional independence using kernel embeddings.
problem Testing conditional independence in high-dimensional settings.
method Analytic kernel embeddings, asymptotic distribution.
result New test outperforms existing methods in high-dimensional settings.
Develops a new asymptotic efficiency theory for non-Euclidean parameter spaces.
problem Lack of a unified efficiency theory for non-Euclidean parameter spaces.
method Introduces a new theory for Riemannian manifolds with regularity conditions.
result Establishes efficiency bounds for non-Euclidean parameter spaces.
Extreme value theory enhances statistical learning extrapolation for rare events.
problem Challenges in traditional machine learning methods for extreme data.
method Asymptotic theory and statistical tools for tail behavior.
result Effective extrapolation methods for extreme quantiles and anomalies.
Improved statistical inference for adaptive Thompson Sampling.
problem Statistical inference challenges in Thompson Sampling.
method Inflating posterior variance in Thompson Sampling.
result Asymptotically normal estimates of arm means with logarithmic regret increase.
The paper addresses statistical estimation in MDPs with confounders using instrumental variables.
problem Statistical estimation of value functions in MDPs with unobservable confounders.
method Two-stage estimator based on instrumental variables for confounded linear MDPs.
result Established statistical properties of the two-stage estimator, including error bounds and asymptotic normality.
Develops asymptotic analysis for RandNLA sampling estimators in least-squares problems.
problem Lack of distributional information for RandNLA estimators in statistical inference.
method Asymptotic analysis of sampling estimators for least-squares problems in two settings.
result Sampling estimators are asymptotically normally distributed under mild conditions.
Paper establishes statistical inference for pairwise comparison models.
problem Statistical inference for pairwise comparison models when the number of subjects diverges.
method Identifies Fisher information matrix as a weighted graph Laplacian for asymptotic normality.
result Near-optimal asymptotic normality result for maximum likelihood estimator.
A method for efficient statistical inference from online algorithms.
problem Computational constraints in online algorithms make traditional variance estimation difficult.
method HulC method that wraps around online algorithms to produce valid confidence regions.
result The HulC method produces asymptotically valid confidence regions for online algorithms.
This paper provides performance guarantees for neural estimation of statistical distances.
problem Developing performance guarantees for neural estimation of statistical distances.
method Non-asymptotic error bounds using function approximation theorems and empirical process theory.
result Established a fundamental tradeoff between approximation and estimation errors in neural estimation of statistical distances.
This paper develops a general framework for analyzing asymptotics of V-statistics. Previous literature on limiting distribution mainly focuses on the cases when n→∞ with fixed kernel size k. Under some regularity conditions, we demonstrate asymptotic normality when k grows with n by utilizing existin…
Study on conditions for achieving optimal robustness in statistical estimators.
problem Achieving the optimal robustness of estimators in statistical models.
method Developed a Wasserstein analogue of the Cramer-Rao inequality and investigated conditions for achieving the Wasserstein-Cramer-Rao lower bound.
result Conditions for the existence of asymptotically efficient estimators in one-parameter models and location-scale families.
Study improves variance calculation for random zero sets on complex manifolds.
problem Improving the variance calculation for random zero sets on complex manifolds.
method Deriving an asymptotic expansion for the variance of linear statistics of zero divisors of random holomorphic sections.
result Sharpens leading-order asymptotics for the variance of random zero sets.
We review basic notions in the field of information geometry such as Fisher metric on statistical manifold, α-connection and corresponding curvature following Amari's work . We show application of information geometry to asymptotic statistical inference.
We derive formulas for F measures' standard error and confidence intervals.
problem Estimating F measures' accuracy with confidence.
method Analytic formulas based on asymptotic normality.
result Valid formulas for sample size planning.
Testing independence is of significant interest in many important areas of large-scale inference. Using extreme-value form statistics to test against sparse alternatives and using quadratic form statistics to test against dense alternatives are two important testing procedures for high-dimensional independence. However…
Paper develops inference methods for low-rank tensors without debiasing.
problem Statistical inference for low-rank tensor models.
method Two-iteration alternating minimization for asymptotic distribution.
result Asymptotic distributions and confidence regions for singular subspaces.
This paper tightens the law of the iterated logarithm for empirical KL_inf, applicable to unbounded data.
problem Developing nonasymptotic concentration bounds for empirical KL_inf with optimal constants and rates.
method Presenting a tight law of the iterated logarithm for empirical KL_inf, applicable to unbounded data.
result A tight law of the iterated logarithm for empirical KL_inf, applicable to unbounded data.
The paper studies quantile contributions and their relationship with order statistics in heavy-tailed distributions.
problem Challenges of classical statistical models in heavy-tailed distributions.
method Theoretical study of quantile contribution statistic and its relationship with order statistics. Derivation of closed-form expression for joint CDF of order statistics and quantile contributions.
result Established asymptotic normality of quantile contributions and characterized their limiting distribution.
This paper introduces time-uniform CLT-based confidence intervals for statistical inference.
problem Developing valid statistical inference methods for sequential data.
method Time-uniform central limit theory and strong invariance principles.
result Asymptotic confidence sequences (CSs) that are uniformly valid over time.
The paper develops approximations for Pearson's chi-square statistic and applies them to confidence intervals.
problem Finding confidence intervals for strictly convex functions of discrete distribution weights.
method Non-asymptotic local normal approximation for multinomial probabilities, deriving bounds and coupling inequalities.
result Developed methods to find confidence intervals for negative entropy of discrete distributions.
Optimal kernel improves estimation accuracy in modal statistical methods.
problem Estimation accuracy of kernel-based modal statistical methods depends on the kernel used.
method The study theoretically shows an optimal kernel that minimizes asymptotic error criterion.
result An optimal kernel minimizes the error criterion when using an optimal bandwidth.
Two new covariance estimators for ROOT-SGD improve statistical inference.
problem Uncertainty measurement for ROOT-SGD's normal distribution estimator.
method Developed two covariance estimators: plug-in and Hessian-free.
result Hessian-free estimator is asymptotically consistent and Hessian-free.
New data improves market impact estimation methods.
problem Improving efficiency of market impact estimation.
method Investigates the use of price trajectory data for market impact estimation.
result Estimation methods using early trade prices outperform established methods asymptotically.
Enhances power of covariance matrix tests for high-dimensional data.
problem Testing large covariance matrices in high-dimensional data.
method Proposes a new Fisher's combined probability test for quadratic form and maximum form statistics.
result Boosts power against more general alternatives.
New method for online statistical inference in contextual bandits using SGD.
problem Online decision-making in contextual bandits with statistical inference.
method Weighted stochastic gradient descent for adaptive data collection.
result Asymptotic normality of the parameter estimator with improved efficiency.
New insights into simple kernel smoothing reveal surprising asymptotics.
problem Understanding precise asymptotics of Nadaraya-Watson kernel smoothing.
method Using ideas from the random energy model in statistical physics.
result Sharp asymptotics for the NW predictor on the sphere.
Overview of high-dimensional time series regression methods.
problem Estimation and inference with high-dimensional time series data.
method Limit theory for high-dimensional dependent data, asymptotic theory for time series regression, statistical learning methods.
result Main limit theory results and asymptotic theory for high-dimensional time series regression.
We revisit resampling procedures for error estimation in binary classification in terms of U-statistics. In particular, we exploit the fact that the error rate estimator involving all learning-testing splits is a U-statistic. Thus, it has minimal variance among all unbiased estimators and is asymptotically normally dis…
Paper bridges statistical inference for DP-SGD, a privacy-preserving machine learning method.
problem Asymptotic statistical inference for Differentially Private Stochastic Gradient Descent (DP-SGD).
method Established asymptotic properties of SGD under randomized subsampling, extended to DP-SGD, proposed methods for constructing valid confidence intervals.
result Valid confidence intervals for DP-SGD output achieve nominal coverage rates while maintaining privacy.
New statistical test for change-point detection using relative entropy.
problem Offline change-point detection using divergence metrics.
method Study of empirical relative entropy distributions, derivation of approximations, introduction of new Berry-Esseen bounds.
result Theoretical and practical validation of relative entropy for change-point detection.
New statistical methods improve TD learning for policy evaluation.
problem Improving statistical inference for reinforcement learning.
method Polyak-Ruppert averaging, refined high-dimensional Berry-Esseen bounds, online plug-in estimator, asymptotic covariance matrix.
result Guaranteed finite-sample coverage of confidence regions and simultaneous confidence intervals.
Unified framework for understanding GRPO as U-statistic.
problem Theoretical properties of GRPO remain less studied.
method Unified framework through classical U-statistics.
result GRPO is asymptotically equivalent to an oracle policy gradient algorithm.
The paper addresses statistical inference issues in adaptive experiments.
problem Statistical inference problems in adaptive experiments.
method Explains and fixes statistical inference issues in adaptive experiments using various methods.
result Various methods to stabilize inferences and recover asymptotic normality.
A new method improves stochastic gradient descent for faster and more efficient estimation.
problem Efficient and fast parametric estimation methods.
method Projected stochastic gradient descent corrected by Fisher scoring.
result The method is faster and more efficient than traditional methods.
Researchers explore statistical perspectives to understand GNN generalization.
problem Limited mathematical understanding of GNN performance.
method Three broad frameworks: learning theory, asymptotics, and random graph models.
result Various theoretical results and open questions identified.