arXiv research

New estimator for symmetric kernel expectations, robust to missing data.

Paper develops efficient incomplete U-statistics for degenerate cases.

Efficient tests for various statistical problems using incomplete U-statistics.

In a wide range of statistical learning problems such as ranking, clustering or metric learning among others, the risk is accurately estimated by $U$-statistics of degree $d\geq 1$, i.e. functionals of the training data with low variance that take the form of averages over $k$-tuples. From a computational perspective, …

The article introduces practical estimators for kernel discrepancies.

Paper introduces a new measure of conditional dependence avoiding matrix inversions.

A scalable ROC-SVM variant reduces training time for imbalanced binary classification.

Subbagging estimation for big data reduces memory usage while maintaining statistical consistency.

Develops an empirical likelihood framework for random forests and ensembles.

This work develops formal statistical inference procedures for machine learning ensemble methods. Ensemble methods based on bootstrapping, such as bagging and random forests, have improved the predictive accuracy of individual trees, but fail to provide a framework in which distributional results can be easily determin…

Paper proposes a method to estimate confidence bands for survival random forests.

Active inference framework improves $U$-statistic estimation efficiency.

This paper simplifies computing higher-order $U$-statistics efficiently.

Improved MoM estimator enhances classical shadows protocol for quantum measurements.

Study on U-statistics with heavy-tailed samples, providing tail bounds and LDP.

U-statistics improve gradient estimation in importance-weighted variational inference.

"Which Generative Adversarial Networks (GANs) generates the most plausible images?" has been a frequently asked question among researchers. To address this problem, we first propose an \emph{incomplete} U-statistics estimate of maximum mean discrepancy $\mathrm{MMD}_{inc}$ to measure the distribution discrepancy betwee…

Measuring divergence between two distributions is essential in machine learning and statistics and has various applications including binary classification, change point detection, and two-sample test. Furthermore, in the era of big data, designing divergence measure that is interpretable and can handle high-dimensiona…

Enhances U-statistics for semi-supervised datasets using unlabeled data.

The paper provides bounds for high-dimensional U-statistics with novel order-explicit inequalities.

High-dimensional U-statistics show surprising phase transitions, impacting kernel-based tests.

New concentration inequality for U-statistics of Markov chains.

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…

Improved estimation of higher order integrals using shrinkage techniques.

Jackknife variance estimation validated for generalized U-statistics.

Unified framework for understanding GRPO as U-statistic.

The paper advances U-statistics in dependent settings, improving spectral estimation and goodness-of-fit tests.

This paper develops dimension-agnostic inference methods for high-dimensional data.

In this paper, we study the problem of computing $U$-statistics of degree $2$, i.e., quantities that come in the form of averages over pairs of data points, in the local model of differential privacy (LDP). The class of $U$-statistics covers many statistical estimates of interest, including Gini mean difference, Kendal…

Proposes a new method to analyze the distributional effects of treatments.

Efficient and robust algorithms for decentralized estimation in networks are essential to many distributed systems. Whereas distributed estimation of sample mean statistics has been the subject of a good deal of attention, computation of $U$-statistics, relying on more expensive averaging over pairs of observations, is…

There has been an increasing interest in testing the equality of large Pearson's correlation matrices. However, in many applications it is more important to test the equality of large rank-based correlation matrices since they are more robust to outliers and nonlinearity. Unlike the Pearson's case, testing the equality…

A new kernel test avoids permutations for independence testing.

We propose a likelihood ratio based inferential framework for high dimensional semiparametric generalized linear models. This framework addresses a variety of challenging problems in high dimensional data analysis, including incomplete data, selection bias, and heterogeneous multitask learning. Our work has three main …

Extends conformal prediction for controlling expected risk of monotone loss functions.

New test assesses probabilistic model calibration without expensive approximations.

New method for MMD with unequal sample sizes improves test power.

SBPMT combines bagging and boosting for improved classification.

USP test improves on Pearson's chi-squared and $G$-test for independence.

Random forests remain among the most popular off-the-shelf supervised learning algorithms. Despite their well-documented empirical success, however, until recently, few theoretical results were available to describe their performance and behavior. In this work we push beyond recent work on consistency and asymptotic no…

This paper develops a general framework for analyzing asymptotics of $V$-statistics. Previous literature on limiting distribution mainly focuses on the cases when $n \to \infty$ with fixed kernel size $k$. Under some regularity conditions, we demonstrate asymptotic normality when $k$ grows with $n$ by utilizing existin…

The method to derive uniform bounds with Gaussian and Rademacher complexities is extended to the case where the sample average is replaced by a nonlinear statistic. Tight bounds are obtained for U-statistics, smoothened L-statistics and error functionals of l2-regularized algorithms.

New unbiased variance estimator for random forests using Hoeffding decomposition.

Unified method for MMD variance estimation improves accuracy and computational efficiency.

New method for efficient matrix completion with nonignorable missing data.

We study the problem of independence testing given independent and identically distributed pairs taking values in a $σ$-finite, separable measure space. Defining a natural measure of dependence $D(f)$ as the squared $L^2$-distance between a joint density $f$ and the product of its marginals, we first show that there is…

Study optimizes KSD estimation from samples, revealing Hilbert-Schmidt vs trace scales.

We quantify uncertainty in Oja's algorithm's leading eigenvector estimation.