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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
Moment-Based Adjustments of Statistical Inference in High...
[Submitted on 28 May 2023 (v1), last revised 25 Aug 2026 (this v · 2023-05-28 · via stat updates on arXiv.org

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Abstract:We develop a statistical inference method for generalized linear models (GLMs) in high-dimensional settings, where the number of unknown coefficients $p$ is of the same order as the sample size $n$. In this regime, constructing confidence intervals requires estimating unknown hyperparameters, such as the signal strength. However, existing estimators for the hyperparameters are not stably applicable to GLMs when $p/n$ is close to or greater than $1$, both theoretically and empirically. In this study, we develop an estimator for the hyperparameter that addresses the issue and establish an inferential framework, provided that the link function of the GLM exhibits an asymmetry property. The proposed estimator utilizes the moments of the output variable of GLMs and a convex surrogate loss. Our framework is theoretically valid even when the limit of $p/n$ exceeds $1$, ensuring the strong consistency of the hyperparameter estimator and asymptotically attaining the exact coverage probability of the confidence intervals. Our numerical experiments support these theoretical results.

Submission history

From: Masaaki Imaizumi [view email]
[v1] Sun, 28 May 2023 14:07:10 UTC (407 KB)
[v2] Tue, 30 May 2023 02:43:31 UTC (407 KB)
[v3] Wed, 25 Oct 2023 15:55:06 UTC (471 KB)
[v4] Thu, 23 May 2024 11:13:26 UTC (1,478 KB)
[v5] Tue, 25 Aug 2026 05:18:43 UTC (463 KB)