Confidence sequences (CSs) based on M-estimation for heavy-tailed, possibly contaminated data.
This repository serves as the code base for the following two papers, both authored by Hongjian Wang and Aaditya Ramdas:
- Catoni-Style Confidence Sequences for Heavy-Tailed Mean Estimation Stochastic Processes and Their Applications
- Huber-robust Confidence Sequences AISTATS 2023 (oral)
The class RCS_generator in robustconfseq.py enables online, sequential, robust estimation (uncertainty quantification) and hypothesis testing of the population mean. One initializes the class by supplying the noise rate eps (can be 0), an upper bound on the variance moment (or any other null hypothesis. Whenever a new datapoint arrives, evoke observe to record it.
In the meantime, one may query the e-value, p-value, and the confidence intervals ad libitum, without worries about the traditionally unsafe behavior of continuous monitoring.
The confidence sequences are proven in both papers minimax optimal.
Related repos:
- confseq: contains CSs for light-tailed data.
- confseq_wor: contains CSs for sampling without replacement.