Sparse Linear Regression With Missing Data
This addresses the problem of handling incomplete datasets in regression for data scientists, but it appears incremental as it builds on existing sparse regression techniques.
The paper tackles sparse linear regression with missing data by proposing a method that jointly learns low-dimensional data structure and sparse coefficients, achieving better performance than competing algorithms in simulations.
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.