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2010/05/10

Presenting an original predictive theory in statistical science

Professor Fumiyasu Komaki
(Department of Mathematical Informatics)

Professor Komaki developed an original predictive theory in statistical science, a field that encompasses broad areas including genetic data, evolution, brain model, pattern recognition such as of character and voice, spatiotemporal data such as global environment, time-series data as in economics, psychology, and natural language processing.

Statistical models are necessary for statistical analysis and there are important basic concepts behind them. Maximum likelihood estimation chooses parameter values maximizing the quantity called likelihood, and Bayes method constructs a probability distribution on the parameter space by setting prior information (prior distribution) and adding likelihood information (new experiments) in order to estimate parameters in models. While the maximum likelihood method uses a point in the parameter space to estimate parameter values, Bayes method uses a probability distribution on the parameter space. Bayes method, however, was criticized for not having “invariance property” and philosophical controversy over invariance continued for decades.

Professor Komaki who has been engaged in both approaches considered that if theoretical performance evaluation were given to maximum likelihood estimation and Bayes methods from the viewpoint of “prediction,” it would become a mathematical problem and the relationship between the two would be convincing. As a result, he demonstrated that Bayes method was better in a sense and also developed a general method to enhance predictions using estimators such as maximum likelihood estimation. By pursuing Bayes method in terms of information geometry framework, the nature of problems is no longer overlooked due to superficial differences. Furthermore, he shed light on what kind of prior probability should be constructed before performing experiments, by looking at information geometric properties of statistical models. This predictive theory is applied to wind velocity analysis, pattern recognition, prediction in track and field, and forecasting insurance claims. Professor Komaki is a diligent mathematical researcher pursuing “universal property” and “invariance property.”


Graduate School of Information Science and Technology
the University of Tokyo