arXiv subjects

Yuepeng Yang

Publications and source records attributed to Yuepeng Yang.

8 recordsLinked to original sources

arXiv2026

Bias-Corrected Subspace Intersection: Minimax-Optimal Shared Subspace Estimation in Multi-View Data

Estimating a low-dimensional subspace shared across noisy data matrices is a fundamental problem in multi-view matrix estimation. We study this problem under the two-view JIVE model, where each data matrix contains shared and view-specific low-rank components. We demonstrate that standard plug-in subspace intersection, including AJIVE, suffers from a second-order bias caused by direction-dependent leakage of the empirical singular vectors. We propose bias-corrected subspace intersection (BCSI), which removes this bias before estimating the shared subspace. We establish finite-sample risk bounds for BCSI that accommodate unequal view dimensions, signal strengths, and view-specific ranks and require no condition-number assumptions on the signal matrices. When the shared and view-specific ranks are comparable, these bounds match our minimax lower bounds up to universal constants. The resulting minimax rate contains a new second-order term, arising from quadratic leakage perturbations relative to the shrinking spectral gap when the view-specific subspaces are nearly aligned. This term is absent from previous JIVE minimax lower bounds. Numerical experiments demonstrate the advantage of BCSI over AJIVE when the leakage bias is pronounced. Along the way, we establish a nonasymptotic concentration result for the bias-corrected leakage Gram matrix of a rectangular spiked matrix, which may be of independent interest.

stat.ME↗

arXiv2026

Robust Average-Reward Markov Decision Processes: Minimax-Optimal Learning via Plug-in Reductions

Distributionally robust Markov decision processes provide a principled framework for sequential decision making under model uncertainty. We study how many samples are necessary and sufficient to learn an $\varepsilon$-optimal robust policy under the average-reward criterion. A generative model provides samples from the nominal transition kernel, whereas policy performance is evaluated over $(s,a)$-rectangular total-variation uncertainty sets of radius at most $\sigma$. Let $H_0$ and $H_\sigma$ denote the nominal and robust optimal bias spans, respectively. We identify $\sigma H_0$ as the perturbation scale separating high- and low-tolerance regimes. Our matching upper and lower bounds show that, up to logarithmic factors, the minimax total sample complexity is $$ NSA \asymp \frac{SA}{\varepsilon^2}\begin{cases} \min\{H_0,H_\sigma\}, & \varepsilon\gtrsim\sigma H_0,\\ \min\{H_0,H_\sigma\}+\sigma H_\sigma^2, & \varepsilon\lesssim\sigma H_0. \end{cases} $$ Here $S$ and $A$ are the numbers of states and actions, and $N$ is the number of samples per state-action pair. The sample complexity consists of a linear-span term that resembles the nominal AMDP results and a robustness-specific term that appears only in the low-tolerance regime. We attain these rates using reduction-based plug-in procedures that select the reduction---nominal or robust---and its discount factor: a span-informed procedure that makes these choices using known span parameters, and a span-agnostic procedure that calibrates both choices from data.

cs.LG↗

arXiv2026

Sample-efficient inductive matrix completion with noise and inexact side-information

Inductive matrix completion (IMC) is a variant of low-rank matrix completion that incorporates row and column side-information. In principle, it can reduce the effective dimension of the recovery problem from the ambient matrix size to the dimension of the side-information features. Existing theory, however, does not fully realize this advantage in the noisy setting: sample-efficient guarantees only apply to noiseless recovery, while noisy guarantees require sample sizes comparable to ordinary matrix completion. This paper closes this gap for noisy IMC. We analyze a nonconvex projected gradient descent algorithm with spectral initialization and prove that, under exact side-information, it achieves linear convergence and stable recovery at a sample complexity governed by the effective side-information dimension rather than the ambient matrix dimension. The key technical ingredient is a local regularity condition for the IMC loss that holds at this reduced sample size, despite the mismatch between the observation pattern and the side-information subspaces. We further extend the analysis to inexact side-information, showing that the same reduced sample complexity is preserved and that the estimation error degrades optimally with the level of subspace misspecification. Motivated by this trade-off, we also propose a penalized interpolation between IMC and ordinary matrix completion that balances sample efficiency against robustness to imperfect side-information. Simulations and experiments on the MovieLens dataset support the theoretical findings and illustrate the practical benefits of exploiting side-information in low-sample regimes.

stat.ML↗

arXiv2025

Random pairing MLE for estimation of item parameters in Rasch model

The Rasch model, a classical model in the item response theory, is widely used in psychometrics to model the relationship between individuals' latent traits and their binary responses to assessments or questionnaires. In this paper, we introduce a new likelihood-based estimator -- random pairing maximum likelihood estimator ($\mathrm{RP\text{-}MLE}$) and its bootstrapped variant multiple random pairing MLE ($\mathrm{MRP\text{-}MLE}$) which faithfully estimate the item parameters in the Rasch model. The new estimators have several appealing features compared to existing ones. First, both work for sparse observations, an increasingly important scenario in the big data era. Second, both estimators are provably minimax optimal in terms of finite sample $\ell_{\infty}$ estimation error. Lastly, both admit precise distributional characterization that allows uncertainty quantification on the item parameters, e.g., construction of confidence intervals for the item parameters. The main idea underlying $\mathrm{RP\text{-}MLE}$ and $\mathrm{MRP\text{-}MLE}$ is to randomly pair user-item responses to form item-item comparisons. This is carefully designed to reduce the problem size while retaining statistical independence. We also provide empirical evidence of the efficacy of the two new estimators using both simulated and real data.

stat.ML↗

arXiv2025

Estimating shared subspace with AJIVE: the power and limitation of multiple data matrices

Integrative data analysis often requires disentangling joint and individual variations across multiple datasets, a challenge commonly addressed by the Joint and Individual Variation Explained (JIVE) model. While numerous methods have been developed to estimate the shared subspace under JIVE, the theoretical understanding of their performance remains limited, particularly in the context of multiple matrices and varying degrees of subspace misalignment. This paper bridges this gap by providing a systematic analysis of shared subspace estimation in multi-matrix settings. We focus on the Angle-based Joint and Individual Variation Explained (AJIVE) method, a two-stage spectral approach, and establish new performance guarantees that uncover its strengths and limitations. Specifically, we show that in high signal-to-noise ratio (SNR) regimes, AJIVE's estimation error decreases with the number of matrices, demonstrating the power of multi-matrix integration. Conversely, in low-SNR settings, AJIVE exhibits a non-diminishing error, highlighting fundamental limitations. To complement these results, we derive minimax lower bounds, showing that AJIVE achieves optimal rates in high-SNR regimes. Furthermore, we analyze an oracle-aided spectral estimator to demonstrate that the non-diminishing error in low-SNR scenarios is a fundamental barrier. Extensive numerical experiments corroborate our theoretical findings, providing insights into the interplay between SNR, the number of matrices, and subspace misalignment.

stat.ML↗

arXiv2024

Top-$K$ ranking with a monotone adversary

In this paper, we address the top-$K$ ranking problem with a monotone adversary. We consider the scenario where a comparison graph is randomly generated and the adversary is allowed to add arbitrary edges. The statistician's goal is then to accurately identify the top-$K$ preferred items based on pairwise comparisons derived from this semi-random comparison graph. The main contribution of this paper is to develop a weighted maximum likelihood estimator (MLE) that achieves near-optimal sample complexity, up to a $\log^2(n)$ factor, where $n$ denotes the number of items under comparison. This is made possible through a combination of analytical and algorithmic innovations. On the analytical front, we provide a refined~$\ell_\infty$ error analysis of the weighted MLE that is more explicit and tighter than existing analyses. It relates the~$\ell_\infty$ error with the spectral properties of the weighted comparison graph. Motivated by this, our algorithmic innovation involves the development of an SDP-based approach to reweight the semi-random graph and meet specified spectral properties. Additionally, we propose a first-order method based on the Matrix Multiplicative Weight Update (MMWU) framework. This method efficiently solves the resulting SDP in nearly-linear time relative to the size of the semi-random comparison graph.

stat.ML↗

arXiv2023

Optimal tuning-free convex relaxation for noisy matrix completion

This paper is concerned with noisy matrix completion--the problem of recovering a low-rank matrix from partial and noisy entries. Under uniform sampling and incoherence assumptions, we prove that a tuning-free square-root matrix completion estimator (square-root MC) achieves optimal statistical performance for solving the noisy matrix completion problem. Similar to the square-root Lasso estimator in high-dimensional linear regression, square-root MC does not rely on the knowledge of the size of the noise. While solving square-root MC is a convex program, our statistical analysis of square-root MC hinges on its intimate connections to a nonconvex rank-constrained estimator.

math.ST↗

arXiv2023

$O(T^{-1})$ Convergence of Optimistic-Follow-the-Regularized-Leader in Two-Player Zero-Sum Markov Games

We prove that optimistic-follow-the-regularized-leader (OFTRL), together with smooth value updates, finds an $O(T^{-1})$-approximate Nash equilibrium in $T$ iterations for two-player zero-sum Markov games with full information. This improves the $\tilde{O}(T^{-5/6})$ convergence rate recently shown in the paper Zhang et al (2022). The refined analysis hinges on two essential ingredients. First, the sum of the regrets of the two players, though not necessarily non-negative as in normal-form games, is approximately non-negative in Markov games. This property allows us to bound the second-order path lengths of the learning dynamics. Second, we prove a tighter algebraic inequality regarding the weights deployed by OFTRL that shaves an extra $\log T$ factor. This crucial improvement enables the inductive analysis that leads to the final $O(T^{-1})$ rate.

cs.LG↗