Outlier-robust Estimation of a Sparse Linear Model Using Invexity
This addresses the robustness issue in sparse linear models for statistical and machine learning applications, though it appears incremental as it builds on existing lasso frameworks.
The paper tackles the problem of estimating sparse regression vectors when outlier samples are present, where standard lasso methods are inconsistent, by proposing a combinatorial outlier-robust lasso that identifies clean samples and uses them for estimation. The result includes a novel invex relaxation with provable theoretical guarantees and experimental validation showing improved performance over standard lasso.
In this paper, we study problem of estimating a sparse regression vector with correct support in the presence of outlier samples. The inconsistency of lasso-type methods is well known in this scenario. We propose a combinatorial version of outlier-robust lasso which also identifies clean samples. Subsequently, we use these clean samples to make a good estimation. We also provide a novel invex relaxation for the combinatorial problem and provide provable theoretical guarantees for this relaxation. Finally, we conduct experiments to validate our theory and compare our results against standard lasso.