# Huber-Robust Confidence Sequences

arXiv: https://arxiv.org/abs/2301.09573 · HTML: https://mlsanity.com/paper/2301.09573/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 49 references that are in the map.
- First posted on arXiv 23 Jan 2023.

## Builds on (most cited first, 17 of 17)

- [Time-uniform, nonparametric, nonasymptotic confidence sequences](https://mlsanity.com/paper/1810.08240/) (2018)
- [Robust Estimators in High Dimensions without the Computational Intractability](https://mlsanity.com/paper/1604.06443/) (2016)
- [Estimating means of bounded random variables by betting](https://mlsanity.com/paper/2010.09686/) (2020)
- [Game-theoretic statistics and safe anytime-valid inference](https://mlsanity.com/paper/2210.01948/) (2022)
- [lil' UCB : An Optimal Exploration Algorithm for Multi-Armed Bandits](https://mlsanity.com/paper/1312.7308/) (2013)
- [Safe Testing](https://mlsanity.com/paper/1906.07801/) (2019)
- [Robust Covariance and Scatter Matrix Estimation under Huber's Contamination Model](https://mlsanity.com/paper/1506.00691/) (2015)
- [High-Dimensional Robust Mean Estimation in Nearly-Linear Time](https://mlsanity.com/paper/1811.09380/) (2018)
- [Robust subgaussian estimation of a mean vector in nearly linear time](https://mlsanity.com/paper/1906.03058/) (2019)
- [Convergence Rates of Stochastic Gradient Descent under Infinite Noise Variance](https://mlsanity.com/paper/2102.10346/) (2021)
- [Testing exchangeability: fork-convexity, supermartingales, and e-processes](https://mlsanity.com/paper/2102.00630/) (2021)
- [Sequential estimation of quantiles with applications to A/B-testing and best-arm identification](https://mlsanity.com/paper/1906.09712/) (2019)
- [Always Valid Inference: Bringing Sequential Analysis to A/B Testing](https://mlsanity.com/paper/1512.04922/) (2015)
- [A framework for Multi-A(rmed)/B(andit) testing with online FDR control](https://mlsanity.com/paper/1706.05378/) (2017)
- [Catoni-style confidence sequences for heavy-tailed mean estimation](https://mlsanity.com/paper/2202.01250/) (2022)
- [A Unified Approach to Robust Mean Estimation](https://mlsanity.com/paper/1907.00927/) (2019)
- [Rapid Regression Detection in Software Deployments through Sequential Testing](https://mlsanity.com/paper/2205.14762/) (2022)

## Built on by (most cited first, 7 of 7)

- [A unified recipe for deriving (time-uniform) PAC-Bayes bounds](https://mlsanity.com/paper/2302.03421/) (2023)
- [Risk-limiting Financial Audits via Weighted Sampling without Replacement](https://mlsanity.com/paper/2305.06884/) (2023)
- [Time-Uniform Confidence Spheres for Means of Random Vectors](https://mlsanity.com/paper/2311.08168/) (2023)
- [Sequential change detection via backward confidence sequences](https://mlsanity.com/paper/2302.02544/) (2023)
- [CRIMED: Lower and Upper Bounds on Regret for Bandits with Unbounded Stochastic Corruption](https://mlsanity.com/paper/2309.16563/) (2023)
- [Online Heavy-tailed Change-point detection](https://mlsanity.com/paper/2306.09548/) (2023)
- [Positive Semidefinite Matrix Supermartingales](https://mlsanity.com/paper/2401.15567/) (2024)

## Abstract (arXiv)

Confidence sequences are confidence intervals that can be sequentially tracked, and are valid at arbitrary data-dependent stopping times. This paper presents confidence sequences for a univariate mean of an unknown distribution with a known upper bound on the p-th central moment (p > 1), but allowing for (at most) ε fraction of arbitrary distribution corruption, as in Huber's contamination model. We do this by designing new robust exponential supermartingales, and show that the resulting confidence sequences attain the optimal width achieved in the nonsequential setting. Perhaps surprisingly, the constant margin between our sequential result and the lower bound is smaller than even fixed-time robust confidence intervals based on the trimmed mean, for example. Since confidence sequences are a common tool used within A/B/n testing and bandits, these results open the door to sequential experimentation that is robust to outliers and adversarial corruptions.