arXiv subjects

Xiaochao Xia

Publications and source records attributed to Xiaochao Xia.

4 recordsLinked to original sources

arXiv2026

Biweighted Poisson Subsampling for Convoluted Rank Regression with Massive Data

Optimal subsampling efficiently selects the most informative data points, enabling accurate statistical inference while significantly reducing computational burden for massive datasets. However, the existing relevant methods can not directly be applied to pairwise loss problems, particularly for convoluted rank regression (CRR), due to the double summation structure in objective function. To this end, we first propose a new BIweighted Poisson Subsampling (BIPS) framework for such problems through designing a proper weight for a pair of observations instead of for a single observation for objective function. Two concrete inverse probability weighting strategies are considered. Secondly, we focus on the CRR models, under which the BIPS estimator (BIPS-CRR) is formulated. We establish consistency and asymptotic normality for BIPS-CRR, derive its optimal Poisson subsampling probabilities under the L-optimality criterion, and provide a practical algorithm to facilitate implementation. Thirdly, we develop a distributed estimator for CRR that incorporates BIPS as a pilot subsampling strategy. This estimation is globally efficient and is robust to both randomly and non-randomly distributed datasets in distributed computing environments. Extensive simulations and a real-world application demonstrate the excellent finite-sample performance of proposed methodology. Additionally, our BIPS can be readily extended to other U-statistics optimization problems and pairwise learning tasks.

math.ST↗

arXiv2024

Distributed Conditional Feature Screening via Pearson Partial Correlation with FDR Control

This paper studies the distributed conditional feature screening for massive data with ultrahigh-dimensional features. Specifically, three distributed partial correlation feature screening methods (SAPS, ACPS and JDPS methods) are firstly proposed based on Pearson partial correlation. The corresponding consistency of distributed estimation and the sure screening property of feature screening methods are established. Secondly, because using a hard threshold in feature screening will lead to a high false discovery rate (FDR), this paper develops a two-step distributed feature screening method based on knockoff technique to control the FDR. It is shown that the proposed method can control the FDR in the finite sample, and also enjoys the sure screening property under some conditions. Different from the existing screening methods, this paper not only considers the influence of a conditional variable on both the response variable and feature variables in variable screening, but also studies the FDR control issue. Finally, the effectiveness of the proposed methods is confirmed by numerical simulations and a real data analysis.

stat.ME↗

arXiv2021

A Robust Partial Correlation-based Screening Approach

As a computationally fast and working efficient tool, sure independence screening has received much attention in solving ultrahigh dimensional problems. This paper contributes two robust sure screening approaches that simultaneously take into account heteroscedasticity, outliers, heavy-tailed distribution, continuous or discrete response, and confounding effect, from the perspective of model-free. First, we define a robust correlation measure only using two random indicators, and introduce a screener using that correlation. Second, we propose a robust partial correlation-based screening approach when an exposure variable is available. To remove the confounding effect of the exposure on both response and each covariate, we use a nonparametric regression with some specified loss function. More specifically, a robust correlation-based screening method (RC-SIS) and a robust partial correlation-based screening framework (RPC-SIS) including two concrete screeners: RPC-SIS(L2) and RPC-SIS(L1), are formed. Third, we establish sure screening properties of RC-SIS for which the response variable can be either continuous or discrete, as well as those of RPC-SIS(L2) and RPC-SIS(L1) under some regularity conditions. Our approaches are essentially nonparametric, and perform robustly for both the response and the covariates. Finally, extensive simulation studies and two applications are carried out to demonstrate the superiority of our proposed approaches.

stat.ME↗

arXiv2018

Copula-based Partial Correlation Screening: a Joint and Robust Approach

Screening for ultrahigh dimensional features may encounter complicated issues such as outlying observations, heteroscedasticity or heavy-tailed distribution, multi-collinearity and confounding effects. Standard correlation-based marginal screening methods may be a weak solution to these issues. We contribute a novel robust joint screener to safeguard against outliers and distribution mis-specification for both the response variable and the covariates, and to account for external variables at the screening step. Specifically, we introduce a copula-based partial correlation (CPC) screener. We show that the empirical process of the estimated CPC converges weakly to a Gaussian process and establish the sure screening property for CPC screener under very mild technical conditions, where we need not require any moment condition, weaker than existing alternatives in the literature. Moreover, our approach allows for a diverging number of conditional variables from the theoretical point of view. Extensive simulation studies and two data applications are included to illustrate our proposal.

math.ST↗