Research Statement

Vadim, 2023

My research focuses on the problems of model selection in Machine Learning. It explores methods of Applied Mathematics and Computer Science. The central problem is selecting the most accurate and robust forecasting model of the simplest structure. To define the algebraic structure of this set according to the application and the origin of data, I use various tools: from tensor algebras to differential geometry. I use multivariate statistics, Bayesian inference, and graph probability to induce the quality criteria of selection. My work joins theory and practical applications. I believe multi-model decoding problems for heterogeneous data are the most promising. Forecasting the variable of a complex structure requires several models to recover dependencies in source and target spaces and to settle the forecast. The examples to investigate are various spatial-time measurements. The practical applications are brain-computer interface, health monitoring with wearable devices, and other signals in biology and physics.