On Binary Statistical Classification from Mismatched Empirically Observed Statistics
Journal
IEEE International Symposium on Information Theory - Proceedings
Journal Volume
2020-June
Pages
2533-2538
Date Issued
2020
Author(s)
Hsu, H.-W.
Abstract
In this paper, we analyze the fundamental limit of statistical classification with mismatched empirically observed statistics. Unlike classical hypothesis testing where we have access to the distributions of data, now we only have two training sequences sampled i.i.d. from two unknown distributions P 0 and P 1 respectively. The goal is to classify a testing sequence sampled i.i.d. from one of the two candidate distributions, each of which is deviated slightly from P 0 and P 1 respectively. In other words, there is mismatch between how the training and testing sequences are generated. The amount of mismatch is measured by the norm of the deviation in the Euclidean space. Assuming the norm of deviation is not greater than δ, we derive an asymptotically optimal test in Chernoff's regime, and analyze its error exponents in both Stein's regime and Chernoff's regime. We also give both upper and lower bounds on the decrease of error exponents due to (i) unknown distributions (ii) mismatch in training and testing distributions. When δ is small, we show that the decrease in error exponents is linear in δ and characterize its first-order term. © 2020 IEEE.
Other Subjects
Errors; Asymptotically optimal; Euclidean spaces; Hypothesis testing; Statistical classification; Testing sequences; Training and testing; Training sequences; Upper and lower bounds; Information theory
Type
conference paper