# Sparse Linear Regression With Missing Data

arXiv: https://arxiv.org/abs/1503.08348 · HTML: https://mlsanity.com/paper/1503.08348/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Mar 2015.

## Built on by (most cited first, 2 of 2)

- [Certain and Approximately Certain Models for Statistical Learning](https://mlsanity.com/paper/2402.17926/) (2024)
- [Learning Over Dirty Data with Minimal Repairs](https://mlsanity.com/paper/2503.13921/) (2025)

## Abstract (arXiv)

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.