Mathematical Programming for Missing Data

Abstract

We propose a mathematical programming method to deal with uncertainty in the observations of a classification problem. This means that we can deal with situations where instead of a sample (xi, yi) we may only have a distribution over (xi, yi) at our disposition. In particular, we derive a robust formulation when the uncertainty is given by a normal distribution. This leads to Second Order Cone Programming Problems. Our method can be applied to the problem of missing data, where it out-performs direct imputation.