Using Empirical Covariance Matrix in Enhancing Prediction Accuracy of Linear Models with Missing Information

TL;DR

This paper proposes a method combining sparse regression and covariance matrix estimation to improve matrix completion and feature selection accuracy in linear models with missing data, leading to reduced prediction error.

Contribution

It introduces a novel approach that integrates empirical covariance matrix estimation with sparse regression to enhance prediction accuracy under missing information.

Findings

Covariance matrix estimation improves matrix completion accuracy.

The proposed method reduces mean squared prediction error.

Simulation results demonstrate performance gains over non-covariance-based methods.

Abstract

Inference and Estimation in Missing Information (MI) scenarios are important topics in Statistical Learning Theory and Machine Learning (ML). In ML literature, attempts have been made to enhance prediction through precise feature selection methods. In sparse linear models, LASSO is well-known in extracting the desired support of the signal and resisting against noisy systems. When sparse models are also suffering from MI, the sparse recovery and inference of the missing models are taken into account simultaneously. In this paper, we will introduce an approach which enjoys sparse regression and covariance matrix estimation to improve matrix completion accuracy, and as a result enhancing feature selection preciseness which leads to reduction in prediction Mean Squared Error (MSE). We will compare the effect of employing covariance matrix in enhancing estimation accuracy to the case it is not used in feature selection. Simulations show the improvement in the performance as compared to the case where the covariance matrix estimation is not used.