Sparse Linear Regression With Missing Data

TL;DR

This paper introduces SLRM, a fast stochastic optimization method for sparse linear regression with missing data, effectively learning data structure and sparse coefficients simultaneously, outperforming existing algorithms.

Contribution

The paper presents a novel scalable algorithm, SLRM, that jointly learns data structure and sparse regression coefficients in the presence of missing data.

Findings

SLRM outperforms competing algorithms on synthetic datasets.

SLRM demonstrates robust performance on real datasets.

Theoretical analysis provides bounds on expected squared loss.

Abstract

This paper proposes a fast and accurate method for sparse regression in the presence of missing data. The underlying statistical model encapsulates the low-dimensional structure of the incomplete data matrix and the sparsity of the regression coefficients, and the proposed algorithm jointly learns the low-dimensional structure of the data and a linear regressor with sparse coefficients. The proposed stochastic optimization method, Sparse Linear Regression with Missing Data (SLRM), performs an alternating minimization procedure and scales well with the problem size. Large deviation inequalities shed light on the impact of the various problem-dependent parameters on the expected squared loss of the learned regressor. Extensive simulations on both synthetic and real datasets show that SLRM performs better than competing algorithms in a variety of contexts.