Evaluation of Error Probability of Classification Based on the Analysis of the Bayes Code: Extension and Example

Saito, Shota; Matsushima, Toshiyasu

doi:10.1109/isit45174.2021.9517718

Cited by 2 publications

(1 citation statement)

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“…There are also studies which take a Bayesian approach. Merhav and Ziv [1] analyzed the weighted sum of type-I and type-II error probabilities, and subsequently, Saito and Matsushima [2,14] gave a different result via the analysis for the Bayes code.…”

Section: Related Workmentioning

confidence: 99%

Analysis on Optimal Error Exponents of Binary Classification for Source with Multiple Subclasses

Kuramata

Yagi

2022

Entropy

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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 P1 and P2. 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 P2 has multiple subclasses but P1 does not. We generalize our results to classification in the case that P1 and P2 are a stationary and memoryless source and a mixed memoryless source with general mixture, respectively.

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Section: Related Workmentioning

confidence: 99%