Optimal Prediction Under Bayesian Decision Theory 

Example of Research 1)：Decision Tree Model

Under the assumption of a data generative model called the “decision tree model,” we derived the optimal prediction based on Bayesian decision theory and constructed an efficient computational algorithm.

Dobashi, Nao, Shota Saito, Yuta Nakahara, and Toshiyasu Matsushima. 2021. "Meta-Tree Random Forest: Probabilistic Data-Generative Model and Bayes Optimal Prediction" Entropy 23, no. 6: 768. https://doi.org/10.3390/e23060768　Link

We study mathematical properties of probability distribution on full rooted trees and rooted trees.

Nakahara, Yuta, Shota Saito, Akira Kamatsuka, and Toshiyasu Matsushima. 2022. "Probability Distribution on Full Rooted Trees" Entropy 24, no. 3: 328. https://doi.org/10.3390/e24030328　Link

Y. Nakahara, S. Saito, A. Kamatsuka and T. Matsushima, "Probability Distribution on Rooted Trees," 2022 IEEE International Symposium on Information Theory (ISIT), Espoo, Finland, 2022, pp. 174-179, doi: 10.1109/ISIT50566.2022.9834481.　Link

Example of Research 2)：Latent Class Model

Murayama, H., Saito, S., Iikubo, Y. et al. Cluster’s Number Free Bayes Prediction of General Framework on Mixture of Regression Models. J Stat Theory Appl 20, 425–449 (2021). https://doi.org/10.1007/s44199-021-00001-5　Link

Ishiwatari, T., Saito, S., Nakahara, Y. et al. Bayes optimal estimation and its approximation algorithm for difference with and without treatment under IRSLC model. Int J Data Sci Anal (2023). https://doi.org/10.1007/s41060-023-00468-8　Link

Lower Bound of Bayes Risk

S. Saito, "Meta-Bound on Lower Bounds of Bayes Risk in Parameter Estimation," IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, 2024, Volume E107.A, Issue 3, Pages 503-509　Link

Evaluation of Error Probability of Classification Based on the Analysis of the Bayes Code

S. Saito and T. Matsushima, "Evaluation of Error Probability of Classification Based on the Analysis of the Bayes Code," 2020 IEEE International Symposium on Information Theory (ISIT), Los Angeles, CA, USA, 2020, pp. 2510-2514, doi: 10.1109/ISIT44484.2020.9173981.　Link

S. Saito and T. Matsushima, "Evaluation of Error Probability of Classification Based on the Analysis of the Bayes Code: Extension and Example," 2021 IEEE International Symposium on Information Theory (ISIT), Melbourne, Australia, 2021, pp. 1445-1450, doi: 10.1109/ISIT45174.2021.9517718.　Link