Choice Prediction With Semidefinite Optimization When Utilities are Correlated

We consider the problem of making choice prediction by optimizing the expectation of maximum utility in discrete choice situations, and propose a discrete choice model which generates choice probabilities through a semidefinite program. The choice model, termed as the cross moment model (CMM) is parsimonious in that it uses only the mean and covariance information of the utilities. It is encouraging that CMM generates reasonable choice estimates when utilities are correlated even though no distributional assumptions on random utilities are made.