(B02-1)　Naito Laboratory
Function Estimation (Smoothing): Many statistical issues can be summarized into a certain estimation problem of function. Important problems include estimation of density function, distribution function, regression function and decision boundary for pattern recognition.
Multivariate Analysis: There have been many researches on “multivariate analysis” in the laboratory, since developing methods for analyzing multivariate data naturally relates to the problems of function estimation. High-dimensional data analysis is also an interesting and important topic.
Machine Learning: The methods of function estimation with algorithm-based “machine learning” approach have been developed in the laboratory as well. From now on, a new research of function estimation with approaches of deep learning will be advanced.

(B02-2)　Nemoto Laboratory
Proofs of mathematical theorems derive from "axioms" using "logic." Axioms are assumptions accepted as true without proof; for instance, the axioms of a group define what a group is. "Logic" determines what conclusions can be drawn from what. For example, the modus ponens rule, "If A then B," and additionally "A," can infer "B," is one of the rules of logic. My research broadly aims to elucidate "what conclusions can be drawn from what axioms and what logic." Furthermore, I classify theorems of ordinary mathematics, such as those of analysis and algebra, from the perspective of necessary and sufficient axioms and logic for proof.