2020 IEEE International Symposium
on Information Theory
21-26 June 2020 • Los Angeles, California, USA
| Paper ID | L.2.1 | ||
| Paper Title | Evaluation of Error Probability of Classification Based on the Analysis of the Bayes Code | ||
| Authors | Shota Saito, Toshiyasu Matsushima, Waseda University, Japan | ||
| Session | L.2: Classification | ||
| Presentation | Lecture | ||
| Track | Statistics and Learning Theory | ||
| Manuscript | Click here to download the manuscript | ||
| Virtual Presentation | Click here to watch in the Virtual Symposium | ||
| Abstract | Suppose that we have two training sequences generated by parametrized distributions $P_{\theta_1^*}$ and $P_{\theta_2^*}$, where $\theta_1^*$ and $\theta_2^*$ are unknown. Given training sequences, we study the problem of classifying whether a test sequence was generated according to $P_{\theta_1^*}$ or $P_{\theta_2^*}$. This problem can be thought of as a hypothesis testing problem and the weighted sum of type-I and type-II error probabilities is analyzed. To prove the results, we utilize the analysis of the codeword lengths of the Bayes code. It is shown that upper and lower bounds of the probability of error are characterized by the terms containing the Chernoff information, the dimension of a parameter space, and the ratio of the length between the training sequences and the test sequence. Further, we generalize the part of the preceding results to multiple hypotheses setup. | ||
Plan Ahead
2021 IEEE International Symposium on Information Theory
11-16 July 2021 | Melbourne, Victoria, Australia
