Statistical Mathematics — Theory and Applications of Statistical Science
 (B03 Araki-lab)
With the rapid development of digital technologies and measurement systems, data has become increasingly complex and diverse. Araki lab focuses on uncovering structure and uncertainty in such data through statistical modeling, aiming to generate new insights and applications. We pursue both theoretical and applied perspectives of statistical science, developing models and methods for parameter estimation and model evaluation using mathematical and machine learning techniques. In functional data analysis, we treat high-dimensional, temporally or spatially structured observations as smooth functions, and design multivariate and machine learning models suited to such data. In biostatistics, we work in close collaboration with medical researchers, handling data from health checkups, blood tests, MRI, and NIRS to develop novel models capable of capturing high-dimensional and dynamic biological patterns. We emphasize the interplay between theory and practice, and value problem discovery through engagement with real-world settings.

 

Medical Image Analysis with Optimization and Machine Learning
 (Yamamoto-lab)
Our research focuses on the development of reconstruction and diagnostic support methods for non-invasive medical imaging data, such as magnetic resonance imaging (MRI), by applying optimization techniques and machine learning. Specifically, we are working on:
image reconstruction methods that enable quantification and visualization of dynamic physiological phenomena, such as metabolism, even from undersampled imaging data constrained by acquisition time and cost; the design of imaging pulse sequences for locally tracking deformations in moving organs such as the myocardium; techniques to harmonize image appearance across different MRI scanners to improve consistency in radiological interpretation and automated analysis; and simulation-based optimization approaches for problems in which the objective function is not explicitly defined and the computational
cost is high. Through these studies, we aim to integrate structural and functional information of living tissues and to develop next-generation image analysis technologies that support clinical decision-making.
 

Clustering　(Dr. Guan Xin)
Clustering is an exploratory statistical analysis method that divides a dataset into several different subgroups without knowing any information about cluster labels of data points. Our research focuses on developing effective clustering methods and optimization algorithms for complex high-dimensional data, as well as analyzing the theoretical properties of these methods.