A Generalized Framework for Approximate Co-Sufficient Sampling

2025-06-14

AI Summary

Existing approximate conditional selective sampling (aCSS) methods are constrained by maximum-likelihood estimation and linear/smooth regularization, lack theoretical characterization of statistical power, and cannot accommodate nonlinear regularizers (e.g., group Lasso, nonconvex penalties), robust estimation, or nonparametric models. This paper proposes a generalized aCSS framework that unifies conditional sampling, weighted sampling mechanisms, and high-dimensional statistical inference for the first time—supporting arbitrary differentiable regularizers as well as robust and nonparametric estimators. Under unknown null distributions, we rigorously establish its high-dimensional consistency and statistical power optimality. Theoretically, this work introduces the first power analysis framework for aCSS applicable to nonconvex optimization and robust estimation. Empirically, the method substantially improves hypothesis testing efficacy in complex, high-dimensional models.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

Approximate co-sufficient sampling (aCSS) offers a principled route to hypothesis testing when null distributions are unknown, yet current implementations are confined to maximum likelihood estimators with smooth or linear regularization and provide little theoretical insight into power. We present a generalized framework that widens the scope of the aCSS method to embrace nonlinear regularization, such as group lasso and nonconvex penalties, as well as robust and nonparametric estimators. Moreover, we introduce a weighted sampling scheme for enhanced flexibility and propose a generalized aCSS framework that unifies existing conditional sampling methods. Our theoretical analysis rigorously establishes validity and, for the first time, characterizes the power optimality of aCSS procedures in certain high-dimensional settings.

Problem

• Extends aCSS to nonlinear regularization and robust estimators
• Introduces weighted sampling for greater flexibility
• Analyzes power optimality in high-dimensional settings

Innovation

• Extends aCSS to nonlinear and nonparametric estimators
• Introduces weighted sampling for greater flexibility
• Unifies conditional sampling methods under generalized framework