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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
Fast Computational Methods for Regularized Estimating Equ...
[Submitted on 26 May 2026] · 2026-05-27 · via stat updates on arXiv.org

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Abstract:Estimating equations arise in a wide range of statistical applications, including longitudinal and clustered data analysis, survival analysis, econometrics, and semiparametric inference. In high-dimensional settings, adding sparsity-inducing regularization often leads to computational challenges that are not fully addressed by standard penalized optimization routines. These challenges are closely tied to the structural form of the underlying estimating problem: mainly, the estimating function needs not be the gradient of a scalar objective and may involve asymmetric Jacobians, overidentification, nonsmoothness, nonconvexity, or nested optimization.
This article first reviews the application areas of estimating equations, and then the computational methods for regularized estimating equations by organizing them into four broad formulations: minimization-type, Dantzig-type, regularization-type, and fixed-point-type approaches. We discuss the main numerical strategies associated with each formulation, including penalized optimization, constrained linear programming, iterative root-solving, and proximal fixed-point iteration. We also highlight the connection between regularized estimating equations and fixed-point problems, which provides a unified computational perspective for analyzing and solving regularized estimating equations.

Submission history

From: Yi Yang [view email]
[v1] Tue, 26 May 2026 01:21:04 UTC (45 KB)