GAAVI: Global Asymptotic Anytime Valid Inference for the Conditional Mean Function

2026-02-08

AI Summary

This work addresses the challenge of conducting anytime-valid, high-confidence inference on conditional mean functions (CMFs) in settings such as adaptive experimentation, optimal treatment allocation, and algorithmic fairness auditing. The authors propose a novel asymptotically anytime-valid statistical test that simultaneously achieves asymptotic Type I error control, power approaching one, and optimal sample complexity relative to the Gaussian location test. Leveraging asymptotic theory, they construct a hypothesis testing framework and employ test inversion to generate functional-valued asymptotic confidence sequences for both CMFs and their contrasts. Empirical evaluations demonstrate that the method maintains nominal error rates across diverse distributions while exhibiting high statistical power, making it well-suited for continuous monitoring applications.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Probabilistic Inference
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• 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
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

Inference on the conditional mean function (CMF) is central to tasks from adaptive experimentation to optimal treatment assignment and algorithmic fairness auditing. In this work, we provide a novel asymptotic anytime-valid test for a CMF global null (e.g., that all conditional means are zero) and contrasts between CMFs, enabling experimenters to make high confidence decisions at any time during the experiment beyond a minimum sample size. We provide mild conditions under which our tests achieve (i) asymptotic type-I error guarantees, (i) power one, and, unlike past tests, (iii) optimal sample complexity relative to a Gaussian location testing. By inverting our tests, we show how to construct function-valued asymptotic confidence sequences for the CMF and contrasts thereof. Experiments on both synthetic and real-world data show our method is well-powered across various distributions while preserving the nominal error rate under continuous monitoring.

Problem

• conditional mean function
• anytime-valid inference
• global null hypothesis
• asymptotic inference
• confidence sequences

Innovation

• anytime-valid inference
• conditional mean function
• asymptotic confidence sequences
• global null testing
• optimal sample complexity