Statistical Inference for Matching Decisions via Matrix Completion under Dependent Missingness

2025-10-30

AI Summary

This paper addresses matrix completion in bilateral matching markets under capacity constraints, where missingness exhibits dependence induced by the matching process—violating standard independent sampling assumptions and undermining estimation and inference accuracy of existing methods. To resolve this, we propose a nonconvex matrix completion algorithm based on Grassmannian gradient descent, integrated with linear debiasing and projection techniques. We establish, for the first time under matching-induced dependence, an asymptotically normal estimator with finite-sample guarantees, applicable to three canonical matching mechanisms. Theoretically, our method achieves near-optimal entrywise convergence rates. Empirically, it accurately estimates agents’ preference parameters, yields valid confidence intervals, and enables efficient statistical evaluation of matching policies.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Mechanism Design

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Economics and fairness of platforms and recommendation systems
• Security and Privacy: Large-scale security measurements

Abstract

This paper studies decision-making and statistical inference for two-sided matching markets via matrix completion. In contrast to the independent sampling assumed in classical matrix completion literature, the observed entries, which arise from past matching data, are constrained by matching capacity. This matching-induced dependence poses new challenges for both estimation and inference in the matrix completion framework. We propose a non-convex algorithm based on Grassmannian gradient descent and establish near-optimal entrywise convergence rates for three canonical mechanisms, i.e., one-to-one matching, one-to-many matching with one-sided random arrival, and two-sided random arrival. To facilitate valid uncertainty quantification and hypothesis testing on matching decisions, we further develop a general debiasing and projection framework for arbitrary linear forms of the reward matrix, deriving asymptotic normality with finite-sample guarantees under matching-induced dependent sampling. Our empirical experiments demonstrate that the proposed approach provides accurate estimation, valid confidence intervals, and efficient evaluation of matching policies.

Problem

• Matrix completion for matching decisions under dependent missingness
• Statistical inference with matching-induced dependent sampling
• Debiasing framework for reward matrix uncertainty quantification

Innovation

• Matrix completion for matching markets with dependent missingness
• Grassmannian gradient descent for non-convex optimization
• Debiasing framework for statistical inference under matching constraints