On Binary Statistical Classification from Mismatched Empirically Observed Statistics

Hsu, Hou-Jun; Wang, I-Hsiang

doi:10.1109/isit44484.2020.9174520

Cited by 8 publications

(4 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In more detail, this condition is required in the proof of the converse part. This condition was also imposed by Gutman [3], Hsu and Wang [4], and Zhou et al [5].…”

Section: Maximum Error Exponentmentioning

confidence: 96%

“…To this end, we generalize Gutman's classifier [3], which was shown to be first-and second-order optimal for memoryless sources (with no multiple subclasses) in [5]. This classifier uses training sequences from one of the two sources, as in [3][4][5], making a type-based decision for a source (subclass) with the smallest skewed Jensen-Shannon divergence [7] among the subclasses. We show that this classifier asymptotically achieves the maximum type-II error exponent in the class of deterministic classifiers for a given pair of distributions when the type-I error probability decays exponentially fast for all pairs of distributions in Theorem 1.…”

Section: Contributionsmentioning

confidence: 99%

“…Ziv [10] proposed a classifier based on empirical entropy and discussed the relationship between binary classification and universal source coding. Hsu and Wang [4] characterized the maximum error exponent with mismatched empirically observed statistics. In their achievability proof, a generalization of Gutman's classifier is also used.…”

Section: Related Workmentioning

confidence: 99%

“…Hypothesis testing includes approaches such as the Bayesian test [1,2] and the Neyman-Pearson test [3][4][5]. In this paper, we take the latter approach to formulate the best asymptotic error exponent (the exponential part of an error probability).…”

Section: Introduction 1backgroundmentioning

confidence: 99%

See 3 more Smart Citations

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

Kuramata

Yagi

2022

Entropy

View full text Add to dashboard Cite

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.

show abstract

“…In more detail, this condition is required in the proof of the converse part. This condition was also imposed by Gutman [3], Hsu and Wang [4], and Zhou et al [5].…”

Section: Maximum Error Exponentmentioning

confidence: 96%