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

arXiv: https://arxiv.org/abs/2602.08096 · HTML: https://mlsanity.com/paper/2602.08096/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 55 references that are in the map.
- First posted on arXiv 8 Feb 2026.

## Builds on (most cited first, 24 of 24)

- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Estimation and Inference of Heterogeneous Treatment Effects using Random Forests](https://mlsanity.com/paper/1510.04342/) (2015)
- [Nonparametric regression using deep neural networks with ReLU activation function](https://mlsanity.com/paper/1708.06633/) (2017)
- [Optimal Best Arm Identification with Fixed Confidence](https://mlsanity.com/paper/1602.04589/) (2016)
- [Time-uniform, nonparametric, nonasymptotic confidence sequences](https://mlsanity.com/paper/1810.08240/) (2018)
- [River: machine learning for streaming data in Python](https://mlsanity.com/paper/2012.04740/) (2020)
- [Hypothesis testing with e-values](https://mlsanity.com/paper/2410.23614/) (2024)
- [Time-uniform central limit theory and asymptotic confidence sequences](https://mlsanity.com/paper/2103.06476/) (2021)
- [Auditing Fairness by Betting](https://mlsanity.com/paper/2305.17570/) (2023)
- [Always Valid Inference: Bringing Sequential Analysis to A/B Testing](https://mlsanity.com/paper/1512.04922/) (2015)
- [FairCanary: Rapid Continuous Explainable Fairness](https://mlsanity.com/paper/2106.07057/) (2021)
- [Treatment Effect Risk: Bounds and Inference](https://mlsanity.com/paper/2201.05893/) (2022)
- [Near-Optimal Non-Parametric Sequential Tests and Confidence Sequences with Possibly Dependent Observations](https://mlsanity.com/paper/2212.14411/) (2022)
- [Peeking with PEAK: Sequential, Nonparametric Composite Hypothesis Tests for Means of Multiple Data Streams](https://mlsanity.com/paper/2402.06122/) (2024)
- [On Stopping Times of Power-one Sequential Tests: Tight Lower and Upper Bounds](https://mlsanity.com/paper/2504.19952/) (2025)
- [Time-Uniform Confidence Spheres for Means of Random Vectors](https://mlsanity.com/paper/2311.08168/) (2023)
- [Reward Maximization for Pure Exploration: Minimax Optimal Good Arm Identification for Nonparametric Multi-Armed Bandits](https://mlsanity.com/paper/2410.15564/) (2024)
- [Anytime-Valid Linear Models and Regression Adjusted Causal Inference in Randomized Experiments](https://mlsanity.com/paper/2210.08589/) (2022)
- [Simulation-Based Inference for Adaptive Experiments](https://mlsanity.com/paper/2506.02881/) (2025)
- [Time-uniform confidence bands for the CDF under nonstationarity](https://mlsanity.com/paper/2302.14248/) (2023)
- [Ensemble methods for testing a global null](https://mlsanity.com/paper/2310.10407/) (2023)
- [CSPI-MT: Calibrated Safe Policy Improvement with Multiple Testing for Threshold Policies](https://mlsanity.com/paper/2408.12004/) (2024)
- [Interactive Martingale Tests for the Global Null](https://mlsanity.com/paper/1909.07339/) (2019)
- [Demistifying Inference after Adaptive Experiments](https://mlsanity.com/paper/2405.01281/) (2024)

## Abstract (arXiv)

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.