Abstract

Recent rapid developments in information technology have enabled the collection of high-dimensional complex data, including in engineering, economics, finance, biology, and health sciences. High-dimensional means that the number of features is large and often far larger than the number of collected data samples (units). In many of these applications, it is desirable to find a small best subset of predictors so that the resulting model has desirable prediction accuracy. In this talk, we present the COMBSS framework, a continuous optimization-based solution that we recently showed to solve the best subset selection problem in linear regression. Then, we highlight how COMBSS can be extended to other models such as the logistic model. Finally, we present how to cast the best subset solution method into principal component analysis and partial least square frameworks.