Construction of estimation methods and their uncertainty quantification methods for high-dimensional count data focusing on structural constraints

2023 Fiscal Year Final Research Report

• Project/Area Number: 19K20222
• Research Category: Grant-in-Aid for Early-Career Scientists
• Allocation Type: Multi-year Fund
• Review Section: Basic Section 60030:Statistical science-related
• Research Institution: The Institute of Statistical Mathematics (2020-2023); The University of Tokyo (2019)
• Principal Investigator: Yano Keisuke 統計数理研究所, 統計基盤数理研究系, 准教授 (20806070)
• Project Period (FY): 2019-04-01 – 2024-03-31
• Keywords: 情報量規準 / ベイズ予測 / MCMC

Outline of Final Research Achievements

This project has established evaluation methods for predictive models based on Bayesian predictive distributions that are applicable to high-dimensional models including count data models. The Widely Applicable Information Criterion (WAIC) has been extensively used for evaluating predictive models based on Bayesian predictive distributions. We demonstrated the theoretical validity of WAIC in high-dimensional models and established efficient computational methods for high-dimensional models, including deep learning. Furthermore, we established an extension of WAIC, the Posterior Covariance Information Criterion (PCIC), which accommodates cases where there are weights on observations, different evaluation functions for predictions and observations, and predictive evaluation functions other than the logarithmic loss.

Free Research Field

統計学

Academic Significance and Societal Importance of the Research Achievements

高次元モデルやカウントデータモデルは諸科学で広く現れる統計モデルである。しかし、その推論法は通常のモデルと比べて十分に定まっているとはいえない。本研究では高次元モデルやカウントデータモデルで利用可能なベイズ予測分布に基づく予測モデルの評価法を確立した。これにより従来はできなかった予測評価(深層学習を含む高次元モデルでの予測評価・観測の重みが存在する場合の予測評価・予測と観測の評価関数が異なる場合の予測評価・対数損失以外の予測評価関数を用いた場合の評価)が可能となった。