arXiv subjects

Haoshu Xu

Publications and source records attributed to Haoshu Xu.

4 recordsLinked to original sources

arXiv2026

Test of partial effects for Frechet regression on Bures-Wasserstein manifolds

We propose a novel test for assessing partial effects in Fréchet regression with responses lying on the Bures-Wasserstein manifold. Under the null hypothesis, we show that the statistic admits a degenerate V-statistic approximation whose limiting distribution is a weighted mixture of chi-squared random variables, with weights determined by the eigenvalues of an integral operator associated with a reproducing kernel Hilbert space (RKHS) kernel. We establish the asymptotic validity and consistency of the proposed test. Its finite-sample performance is examined through simulation studies. We apply the proposed test to study the effect of age, while controlling for other covariates, on gene co-expression structure in single-cell data.

stat.ML↗

arXiv2026

Inference and Uncertainty Quantification for Streaming $r$-PCA

We address two open questions in streaming PCA via Oja's algorithm: sharp operator-norm convergence for general rank under sub-Gaussian data, and distributional inference for the resulting subspace estimator. Existing convergence analyses, even in the rank-one case, either assume bounded data or leave non-vanishing remainder terms that prevent adaptation to a polynomially vanishing tail spectrum, while existing distributional results are confined to the rank-one case. Our convergence theory removes these remainder terms and yields a sharp rate. In the dense-tail spiked covariance regime, this rate matches the minimax rate up to logarithmic factors. More generally, we prove a matching lower bound, up to logarithmic factors, across both dense-tail and sparse-tail regimes under a mild nondegeneracy condition. The analysis yields a linearization of Oja's iterates, which in turn enables a high-dimensional Gaussian approximation for the general-rank subspace estimation error with an explicit limiting covariance. We also establish a row-wise Gaussian approximation over convex sets for the aligned difference, recovering prior rank-one results as special cases. For practical inference, we develop an online multiplier bootstrap algorithm and prove its consistency. Beyond streaming PCA, our techniques contribute to Gaussian approximation and bootstrap inference for nonconvex stochastic approximation.

stat.ML↗

arXiv2025

A Practical Theory of Generalization in Selectivity Learning

Query-driven machine learning models have emerged as a promising estimation technique for query selectivities. Yet, surprisingly little is known about the efficacy of these techniques from a theoretical perspective, as there exist substantial gaps between practical solutions and state-of-the-art (SOTA) theory based on the Probably Approximately Correct (PAC) learning framework. In this paper, we aim to bridge the gaps between theory and practice. First, we demonstrate that selectivity predictors induced by signed measures are learnable, which relaxes the reliance on probability measures in SOTA theory. More importantly, beyond the PAC learning framework (which only allows us to characterize how the model behaves when both training and test workloads are drawn from the same distribution), we establish, under mild assumptions, that selectivity predictors from this class exhibit favorable out-of-distribution (OOD) generalization error bounds. These theoretical advances provide us with a better understanding of both the in-distribution and OOD generalization capabilities of query-driven selectivity learning, and facilitate the design of two general strategies to improve OOD generalization for existing query-driven selectivity models. We empirically verify that our techniques help query-driven selectivity models generalize significantly better to OOD queries both in terms of prediction accuracy and query latency performance, while maintaining their superior in-distribution generalization performance.

stat.ML↗

arXiv2024

Wasserstein F-tests for Fréchet regression on Bures-Wasserstein manifolds

This paper considers the problem of regression analysis with random covariance matrix as outcome and Euclidean covariates in the framework of Fréchet regression on the Bures-Wasserstein manifold. Such regression problems have many applications in single cell genomics and neuroscience, where we have covariance matrix measured over a large set of samples. Fréchet regression on the Bures-Wasserstein manifold is formulated as estimating the conditional Fréchet mean given covariates $x$. A non-asymptotic $\sqrt{n}$-rate of convergence (up to $\log n$ factors) is obtained for our estimator $\hat{Q}_n(x)$ uniformly for $\left\|x\right\| \lesssim \sqrt{\log n}$, which is crucial for deriving the asymptotic null distribution and power of our proposed statistical test for the null hypothesis of no association. In addition, a central limit theorem for the point estimate $\hat{Q}_n(x)$ is obtained, giving insights to a test for covariate effects. The null distribution of the test statistic is shown to converge to a weighted sum of independent chi-squares, which implies that the proposed test has the desired significance level asymptotically. Also, the power performance of the test is demonstrated against a sequence of contiguous alternatives. Simulation results show the accuracy of the asymptotic distributions. The proposed methods are applied to a single cell gene expression data set that shows the change of gene co-expression network as people age.

stat.ME↗