  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.
