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A Refined Generalization Analysis for Extreme Multi-class Supervised Contrastive Representation Learning Ensemble Distributionally Robust Bayesian Optimisation The Proxy Presumption: From Semantic Embeddings to Valid Social Measures Modulated learning for private and distributed regression with just a single sample per client device Query-efficient model evaluation using cached responses Functional-prior-based approaches to Bayesian PDE-constrained inversion using physics-informed neural networks Optimal Experiments for Partial Causal Effect Identification Order-Agnostic Autoregressive Modelling with Missing Data Grokking or Glitching? How Low-Precision Drives Slingshot Loss Spikes Tuning Derivatives for Causal Fairness in Machine Learning Spherical Flows for Sampling Categorical Data Bayesian Rain Field Reconstruction using Commercial Microwave Links and Diffusion Model Priors GRALIS: A Unified Canonical Framework for Linear Attribution Methods via Riesz Representation Sharp Capacity Thresholds in Linear Associative Memory: From Winner-Take-All to Listwise Retrieval Unified Framework of Distributional Regret in Multi-Armed Bandits and Reinforcement Learning Jacobian-Velocity Bounds for Deployment Risk Under Covariate Drift Self-Attention as Transport: Limits of Symmetric Spectral Diagnostics Perturbation is All You Need for Extrapolating Language Models Adapt or Forget: Provable Tradeoffs Between Adam and SGD in Nonstationary Optimization Realizable Bayes-Consistency for General Metric Losses Graph Convolutional Support Vector Regression for Robust Spatiotemporal Forecasting of Urban Air Pollution Segmenting Human-LLM Co-authored Text via Change Point Detection Stochastic Schrödinger Diffusion Models for Pure-State Ensemble Generation Understanding Self-Supervised Learning via Latent Distribution Matching The Geometric Mechanics of Contrastive Representation Learning: Alignment Potentials, Entropic Dispersion, and Cross-modal Divergence Imbalanced Classification under Capacity Constraints On the Spectral Structure and Objective Equivalence of Orthogonal Multilabel Fisher Discriminants Partially Observed Structural Causal Models First-Order Efficiency for Probabilistic Value Estimation via A Statistical Viewpoint Robust and Fast Training via Per-Sample Clipping
Linear quasi-shrinkage estimator for high-dimensional opt...
[Submitted on 28 Feb 2024 (v1), last revised 8 Sep 2026 (this ve · 2024-02-29 · via stat updates on arXiv.org

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Abstract:In large-scale data-driven optimization problems, parameters are often only known approximately due to noisy and small-sized samples. We consider optimization problems with linear constraints where the true parameter matrix is not precisely known, and the number of constraints and variables are comparable and large. Our goal is to construct a linear estimator of the true parameter matrix by minimizing the Frobenius distance between the estimator and the true parameter matrix. Our method offers three key advantages: 1) the coefficients of the linear estimator are consistently estimated from the observations and require no further calibration; 2) it only requires the sample size to be greater than one and it delivers stable performance across varied sample sizes; and 3) the constraints of the formulated optimization problem using the estimator remain linear, ensuring computational efficiency when the number of constraints and variables are large. Simulation shows that our linear estimator consistently produces stable outcomes in terms of the objective value, the ratio of violated constraints and the magnitude of constraint violation across various scenarios, compared to the nominal and robust methods. Additionally, it demonstrates resilience against high levels of noise, making it a robust choice under uncertainty.

Submission history

From: Naqi Huang [view email]
[v1] Wed, 28 Feb 2024 19:21:38 UTC (1,719 KB)
[v2] Tue, 8 Sep 2026 11:17:59 UTC (3,211 KB)