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- Title
Analysis on Optimal Error Exponents of Binary Classification for Source with Multiple Subclasses.
- Authors
Kuramata, Hiroto; Yagi, Hideki
- Abstract
We consider a binary classification problem for a test sequence to determine from which source the sequence is generated. The system classifies the test sequence based on empirically observed (training) sequences obtained from unknown sources P 1 and P 2 . We analyze the asymptotic fundamental limits of statistical classification for sources with multiple subclasses. We investigate the first- and second-order maximum error exponents under the constraint that the type-I error probability for all pairs of distributions decays exponentially fast and the type-II error probability is upper bounded by a small constant. In this paper, we first give a classifier which achieves the asymptotically maximum error exponent in the class of deterministic classifiers for sources with multiple subclasses, and then provide a characterization of the first-order error exponent. We next provide a characterization of the second-order error exponent in the case where only P 2 has multiple subclasses but P 1 does not. We generalize our results to classification in the case that P 1 and P 2 are a stationary and memoryless source and a mixed memoryless source with general mixture, respectively.
- Subjects
EXPONENTS; ERROR probability; ERROR rates; CLASSIFICATION; TEST systems
- Publication
Entropy, 2022, Vol 24, Issue 5, pN.PAG
- ISSN
1099-4300
- Publication type
Article
- DOI
10.3390/e24050635