# Exponentially Consistent Statistical Classification of Continuous Sequences with Distribution Uncertainty

arXiv: https://arxiv.org/abs/2410.21799 · HTML: https://mlsanity.com/paper/2410.21799/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 25 references that are in the map.
- First posted on arXiv 29 Oct 2024.

## Builds on (most cited first, 4 of 4)

- [Kernel Robust Hypothesis Testing](https://mlsanity.com/paper/2203.12777/) (2022)
- [Second-Order Asymptotically Optimal Statistical Classification](https://mlsanity.com/paper/1806.00739/) (2018)
- [Sequential Classification with Empirically Observed Statistics](https://mlsanity.com/paper/1912.01170/) (2019)
- [Linear-Complexity Exponentially-Consistent Tests for Universal Outlying Sequence Detection](https://mlsanity.com/paper/1701.06084/) (2017)

## Abstract (arXiv)

In multiple classification, one aims to determine whether a testing sequence is generated from the same distribution as one of the M training sequences or not. Unlike most of existing studies that focus on discrete-valued sequences with perfect distribution match, we study multiple classification for continuous sequences with distribution uncertainty, where the generating distributions of the testing and training sequences deviate even under the true hypothesis. In particular, we propose distribution free tests and prove that the error probabilities of our tests decay exponentially fast for three different test designs: fixed-length, sequential, and two-phase tests. We first consider the simple case without the null hypothesis, where the testing sequence is known to be generated from a distribution close to the generating distribution of one of the training sequences. Subsequently, we generalize our results to a more general case with the null hypothesis by allowing the testing sequence to be generated from a distribution that is vastly different from the generating distributions of all training sequences.