For international students who are interested in SEI's laboratory

In what follows, I briefly describe research topics I am interested in recently. Students may study any other topics. (September, 2015)
• Terminology
Directional Statistics: Statistics for data on spheres, rotation groups and so on.
Algebraic Statistics: An approach to computational problems in statistics by use of polynomial rings etc.
Statistical Model: A set of probability distributions to explain data.
Statistical models for directional statistics often contain an integral which is hard to compute. Even for such models, if the integral is a holonomic function, the computational cost may be reduced. We apply the method to specific statistical models and study its characteristics.
2. Statistical Model using Optimal Transport (Gradient Modeling)
There is an idea to use transformation for avoiding integration in statistical models. In particular, transformation called optimal transport is flexible and relatively easy to compute. A problem is that the model is hard to interpret. We study its possibility and limitation.
3. Imbalanced Data and Deformed Exponential Family
An imbalanced data refers to a data with a small number of positive cases and a large number of negative cases. We showed that, if a binomial regression model is applied to such data, then the model converges to a deformed exponential family. The deformed exponential family has relation with statistical physics and information geometry.

Research subjects of graduate students I supervised

From 2011 to 2014, I was in Dept. of Mathematics, Keio University.
• 2014
Master's thesis (in Japanese)
Residual analysis of spatial point processes data
Analysis of calligraphic data: quantification of similarity to a model
Holonomic gradient method for multivariate alternative t-distribution
Information-geometric interpretation of copula model