Greedy control group selection for multi-explanatory multi-output regression problem

Abstract

Abstract The problem of multi-output learning involves the simultaneous prediction of multiple outputs based on given inputs. This paper focuses on addressing this challenge, assuming that we can only monitor a subset of variables. This resource constraint led to a definition of a new kind of problem, that we call Multi-Explanatory Multi-Output Regression (MEMOR) task. The goal of MEMOR is to select explanatory variables that minimize the prediction error for target variables. The central question pertains to the optimal choice of a given number of variables to maximize the goodness of the regression. We propose two greedy approaches for identifying good explanatory variables, along with a linear approximation as a baseline. To evaluate the performance of the proposed algorithms, we compared the resulting explanatory variables with the optimal set obtained through an exhaustive search. Our greedy algorithms surpass the linear method with better regression results, while they are faster than the exhausted method. Both the MEMOR problem and the methods developed for it are well-suited for multi-dimensional data analysis with resource constraints.