Second order cone programming approaches for handling missing and uncertain data

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

Structured Prediction with Relative Margin

In structured prediction problems, outputs are not confined to binary labels; they are often complex objects such as sequences, trees, or alignments. Support Vector Machine (SVM) methods have been successfully extended to such prediction problems. However, recent developments in large margin methods show that higher order information can be exploited for even better generalization. This article first points out a shortcoming of the SVM approach for the structured prediction; an efficient formulation is then presented to overcome the problem. The proposed algorithm exploits the fact that both the minimum and the maximum of quantities of interest are often efficiently computable even though quantities such as mean, median and variance may not be. The resulting formulation produces state-of-the-art performance on sequence learning problems. Dramatic improvements are also seen on multi-class problems.