Statistical Inference for Matching Decisions via Matrix Completion under Dependent Missingness

• URL: http://arxiv.org/abs/2510.26478v1
• Date: Thu, 30 Oct 2025 13:31:32 GMT
• Title: Statistical Inference for Matching Decisions via Matrix Completion under Dependent Missingness
• Authors: Congyuan Duan, Wanteng Ma, Dong Xia, Kan Xu,
• Abstract summary: We propose an algorithm for non-optimal entry for three canonical mechanisms, i.e. one-to-one, one-sided matching with one-sided random arrival, and two-sided random arrival.<n>Our empirical experiments demonstrate that the proposed approach provides accurate estimation valid confidence intervals and efficient evaluation.
• Score: 6.28693385008859
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

Related papers

• Match Made with Matrix Completion: Efficient Learning under Matching Interference [3.4439950003681417]
  We show that standard nuclear norm regularization remains theoretically effective under matching interference.<n>We develop a novel double-enhanced'' estimator, based off the nuclear norm estimator, with a near-optimal entry-wise guarantee.
  arXiv  Detail & Related papers  (2026-01-11T16:33:01Z)
• Testing for latent structure via the Wilcoxon--Wigner random matrix of normalized rank statistics [0.20052993723676893]
  We introduce and systematically study certain symmetric matrices, called Wilcoxon--Wigner random matrices.<n>We establish that the leading eigenvalue and corresponding eigenvector of Wilcoxon--Wigner random matrices admit fluctuations with explicit scaling terms.<n>Results enable rigorous parameter-free and distribution-free spectral methodology for addressing two hypothesis testing problems.
  arXiv  Detail & Related papers  (2025-12-21T23:49:22Z)
• A Principled Approach to Randomized Selection under Uncertainty: Applications to Peer Review and Grant Funding [61.86327960322782]
  We propose a principled framework for randomized decision-making based on interval estimates of the quality of each item.<n>We introduce MERIT, an optimization-based method that maximizes the worst-case expected number of top candidates selected.<n>We prove that MERIT satisfies desirable axiomatic properties not guaranteed by existing approaches.
  arXiv  Detail & Related papers  (2025-06-23T19:59:30Z)
• Assumption-Lean Post-Integrated Inference with Surrogate Control Outcomes [6.448728765953916]
  We introduce a robust post-integrated inference (PII) method that adjusts for latent heterogeneity using control outcomes.<n>We develop semiparametric inference on projected direct effect estimands, accounting for hidden mediators, confounders, and moderators.<n>The proposed doubly robust estimators are consistent and efficient under minimal assumptions and potential misspecification.
  arXiv  Detail & Related papers  (2024-10-07T12:52:38Z)
• Probabilistic Conformal Prediction with Approximate Conditional Validity [81.30551968980143]
  We develop a new method for generating prediction sets that combines the flexibility of conformal methods with an estimate of the conditional distribution. Our method consistently outperforms existing approaches in terms of conditional coverage.
  arXiv  Detail & Related papers  (2024-07-01T20:44:48Z)
• Regularized Projection Matrix Approximation with Applications to Community Detection [1.3761665705201904]
  This paper introduces a regularized projection matrix approximation framework designed to recover cluster information from the affinity matrix. We investigate three distinct penalty functions, each specifically tailored to address bounded, positive, and sparse scenarios. Numerical experiments conducted on both synthetic and real-world datasets reveal that our regularized projection matrix approximation approach significantly outperforms state-of-the-art methods in clustering performance.
  arXiv  Detail & Related papers  (2024-05-26T15:18:22Z)
• Mitigating LLM Hallucinations via Conformal Abstention [70.83870602967625]
  We develop a principled procedure for determining when a large language model should abstain from responding in a general domain. We leverage conformal prediction techniques to develop an abstention procedure that benefits from rigorous theoretical guarantees on the hallucination rate (error rate) Experimentally, our resulting conformal abstention method reliably bounds the hallucination rate on various closed-book, open-domain generative question answering datasets.
  arXiv  Detail & Related papers  (2024-04-04T11:32:03Z)
• Mixed Matrix Completion in Complex Survey Sampling under Heterogeneous Missingness [6.278498348219109]
  We propose a fast and scalable estimation algorithm that achieves sublinear convergence. The proposed method is applied to analyze the National Health and Nutrition Examination Survey data.
  arXiv  Detail & Related papers  (2024-02-06T12:26:58Z)
• Learning with Complementary Labels Revisited: The Selected-Completely-at-Random Setting Is More Practical [66.57396042747706]
  Complementary-label learning is a weakly supervised learning problem. We propose a consistent approach that does not rely on the uniform distribution assumption. We find that complementary-label learning can be expressed as a set of negative-unlabeled binary classification problems.
  arXiv  Detail & Related papers  (2023-11-27T02:59:17Z)
• Likelihood Ratio Confidence Sets for Sequential Decision Making [51.66638486226482]
  We revisit the likelihood-based inference principle and propose to use likelihood ratios to construct valid confidence sequences. Our method is especially suitable for problems with well-specified likelihoods. We show how to provably choose the best sequence of estimators and shed light on connections to online convex optimization.
  arXiv  Detail & Related papers  (2023-11-08T00:10:21Z)
• Exploiting Observation Bias to Improve Matrix Completion [15.171759590760574]
  We propose a natural model where the observation pattern and outcome of interest are driven by the same set of underlying latent (or unobserved) factors.<n>We devise Mask Nearest Neighbor (MNN), a novel two-stage matrix completion algorithm.<n>Our analysis reveals that MNN enjoys entry-wise finite-sample error rates that are competitive with corresponding supervised learning parametric rates.
  arXiv  Detail & Related papers  (2023-06-07T20:48:35Z)
• Random Forest Weighted Local Fréchet Regression with Random Objects [18.128663071848923]
  We propose a novel random forest weighted local Fr'echet regression paradigm.<n>Our first method uses these weights as the local average to solve the conditional Fr'echet mean.<n>Second method performs local linear Fr'echet regression, both significantly improving existing Fr'echet regression methods.
  arXiv  Detail & Related papers  (2022-02-10T09:10:59Z)
• Slice Sampling for General Completely Random Measures [74.24975039689893]
  We present a novel Markov chain Monte Carlo algorithm for posterior inference that adaptively sets the truncation level using auxiliary slice variables. The efficacy of the proposed algorithm is evaluated on several popular nonparametric models.
  arXiv  Detail & Related papers  (2020-06-24T17:53:53Z)
• Robust Matrix Completion with Mixed Data Types [0.0]
  We consider the problem of recovering a structured low rank matrix with partially observed entries with mixed data types. Most approaches assume that there is only one underlying distribution and the low rank constraint is regularized by the matrix Schatten Norm. We propose a computationally feasible statistical approach with strong recovery guarantees along with an algorithmic framework suited for parallelization to recover a low rank matrix with partially observed entries for mixed data types in one step.
  arXiv  Detail & Related papers  (2020-05-25T21:35:10Z)
• Asymptotic Analysis of an Ensemble of Randomly Projected Linear Discriminants [94.46276668068327]
  In [1], an ensemble of randomly projected linear discriminants is used to classify datasets. We develop a consistent estimator of the misclassification probability as an alternative to the computationally-costly cross-validation estimator. We also demonstrate the use of our estimator for tuning the projection dimension on both real and synthetic data.
  arXiv  Detail & Related papers  (2020-04-17T12:47:04Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.