Second Order Cone Programming Approaches for Handling Missing and Uncertain Data

Abstract

We propose a novel second order cone programming formulation for designing robust classifiers
\nwhich can handle uncertainty in observations. Similar formulations are also derived for designing
\nregression functions which are robust to uncertainties in the regression setting. The proposed formulations
\nare independent of the underlying distribution, requiring only the existence of second order
\nmoments. These formulations are then specialized to the case of missing values in observations
\nfor both classification and regression problems. Experiments show that the proposed formulations
\noutperform imputation.