arXiv subjects

Kangqiang Li

Publications and source records attributed to Kangqiang Li.

6 recordsLinked to original sources

arXiv2026

Byzantine-Robust Distributed Sparse Learning Revisited

We revisit Byzantine robust distributed estimation for high-dimensional sparse linear models. By combining local $\ell_1$-regularized robust estimation with robust aggregation at the server, the framework applies to pseudo-Huber regression, quantile regression, and sparse SVM. We show that the resulting estimators yield non-asymptotic guarantees and attain near-optimal statistical rates under mild conditions, while remaining communication-efficient. Simulations confirm strong robustness in estimation, support recovery and classification accuracy under various Byzantine attacks.

cs.LG↗

arXiv2026

Bayesian Smoothed Quantile Regression

The standard asymmetric Laplace framework for Bayesian quantile regression (BQR) suffers from a fundamental decision-theoretic misalignment, yielding biased finite-sample estimates, and precludes gradient-based computation due to non-smoothness. We propose Bayesian smoothed quantile regression (BSQR), a principled framework built on a kernel-smoothed, fully differentiable likelihood. Methodologically, the symmetrizing property of our objective reduces inferential bias and aligns the posterior mean with the true conditional quantile. Theoretically, we establish posterior consistency and a Bernstein--von Mises theorem under misspecification, delivering asymptotic normality and valid frequentist coverage via a generalized Wilks phenomenon, while guaranteeing global posterior existence unlike empirical likelihood approaches. Computationally, BSQR enables Hamiltonian Monte Carlo for BQR, alleviating high-dimensional mixing bottlenecks. In simulations, BSQR reduces out-of-sample prediction error by up to 50% and improves sampling efficiency by up to 80% relative to asymmetric Laplace benchmarks, with uniform and triangular kernels performing particularly well. In a financial application to asymmetric systemic risk, BSQR uncovers distinct regime shifts around the COVID-19 period and yields sharper yet well-calibrated predictive quantiles, underscoring its practical relevance.

stat.ME↗

arXiv2025

Robust low-rank tensor regression via clipping and Huber loss

In this paper, we construct a parameter estimation framework for robust low-rank tensor regression based on a truncation method and Huber loss, specifically focusing on models with random noise having only finite second-order moments. Through a robust gradient descent method, our proposed Huber-type estimator is theoretically optimal in two aspects: (1) its statistical error rate matches the optimal upper bound established for the traditional least squares method under sub-Gaussian error; and (2) the sample complexity for recovering the tensor parameter is also optimal. Extensive numerical experiments demonstrate the robustness of our estimator, indicating that the utilization of truncation and Huber loss significantly enhances stability and statistical effectiveness, outperforming the traditional least squares method. Additionally, the phenomenon of phase transition in the convergence rate of the proposed estimator is confirmed through simulation. Furthermore, applications to image recovery and the Beijing air-quality dataset demonstrate the practical effectiveness of our method.

math.ST↗

arXiv2023

Two Results on Low-Rank Heavy-Tailed Multiresponse Regressions

This paper gives two theoretical results on estimating low-rank parameter matrices for linear models with multivariate responses. We first focus on robust parameter estimation of low-rank multi-task learning with heavy-tailed data and quantization scenarios. It comprises two cases: quantization under heavy-tailed responses and quantization with both heavy-tailed covariate and response variables. For each case, our theory shows that the proposed estimator has a minmax near-optimal convergence rate. We then further investigate low-rank linear models with heavy-tailed matrix-type responses. The theory shows that when the random noise has only $(2+ε)$-order moment, our robust estimator still has almost the same statistical convergence rate as that of sub-Gaussian data. Moreover, our simulation experiments confirm the correctness of theories and show the superiority of our estimators.

math.ST↗

arXiv2022

Robust parameter estimation of regression model under weakened moment assumptions

This paper provides some extended results on estimating parameter matrix of several regression models when the covariate or response possesses weaker moment condition. We study the $M$-estimator of Fan et al. (Ann Stat 49(3):1239--1266, 2021) for matrix completion model with $(1+ε)$-th moment noise. The corresponding phase transition phenomenon is observed. When $1> ε>0$, the robust estimator possesses a slower convergence rate compared with previous literature. For high dimensional multiple index coefficient model, we propose an improved estimator via applying the element-wise truncation method to handle heavy-tailed data with finite fourth moment. The extensive simulation study validates our theoretical results.

math.ST↗

arXiv2021

Robust covariance estimation for distributed principal component analysis

Fan et al. [$\mathit{Annals}$ $\mathit{of}$ $\mathit{Statistics}$ $\textbf{47}$(6) (2019) 3009-3031] constructed a distributed principal component analysis (PCA) algorithm to reduce the communication cost between multiple servers significantly. However, their algorithm's guarantee is only for sub-Gaussian data. Spurred by this deficiency, this paper enhances the effectiveness of their distributed PCA algorithm by utilizing robust covariance matrix estimators of Minsker [$\mathit{Annals}$ $\mathit{of}$ $\mathit{Statistics}$ $\textbf{46}$(6A) (2018) 2871-2903] and Ke et al. [$\mathit{Statistical}$ $\mathit{Science}$ $\textbf{34}$(3) (2019) 454-471] to tame heavy-tailed data. The theoretical results demonstrate that when the sampling distribution is symmetric innovation with the bounded fourth moment or asymmetric with the finite $6$-th moment, the statistical error rate of the final estimator produced by the robust algorithm is similar to that of sub-Gaussian tails. Extensive numerical trials support the theoretical analysis and indicate that our algorithm is robust to heavy-tailed data and outliers.

math.ST↗