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. Our paper has been accepted at the International Conference on Artificial Intelligence and Statistics (AISTATS).

• Yuta Nakahara, Shota Saito, Naoki Ichijo, Koki Kazama, Toshiyasu Matsushima, "Bayesian Decision Theory on Decision Trees: Uncertainty Evaluation and Interpretability,"  Proceedings of The 28th International Conference on Artificial Intelligence and Statistics (AISTATS), PMLR 258:1045-1053, 2025.　Link
• Nao Dobashi, 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 the mathematical properties of probability distributions on full rooted trees and rooted trees.

• Yuta Nakahara, Shota Saito, Akira Kamatsuka, Toshiyasu Matsushima, "Probability Distribution on Rooted Trees: Generalization from Full Trees," IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, 2026, Volume E109.A, Issue 3, Pages 524-537.　Link
• Yuta Nakahara, Shota Saito, Akira Kamatsuka, Toshiyasu Matsushima. 2022. "Probability Distribution on Full Rooted Trees" Entropy 24, no. 3: 328. https://doi.org/10.3390/e24030328　Link
• Yuta Nakahara, Shota Saito, Akira Kamatsuka, Toshiyasu 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

We derived optimal predictions based on Bayesian decision theory under a data generation and observation mechanism that assumes latent classes. We also developed an algorithm to perform approximate calculations of these optimal predictions.

• 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

Estimating the parameters of a probability distribution from data is a fundamental and critical problem in statistics and machine learning. One metric used to measure the “quality” of parameter estimation is “Bayesian risk.” This is a measure that represents the average error between the true parameter value and the estimated value; generally, the smaller the Bayesian risk, the less error the estimate is expected to have on average. In this study, we proposed a formula called “Meta-Bound” from an information-theoretic perspective, demonstrated that various existing theoretical results can be derived from this formula, and provided a unified framework for understanding the existing research.

• Shota 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

We have demonstrated that by utilizing theoretical analysis methods for Bayes codes, it is possible to evaluate the classification error in classification problems.

• Shota Saito and Toshiyasu 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
• Shota Saito and Toshiyasu 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