Utility Based Model Selection and Model Averaging
Seminar | November 20 | 3:10-4 p.m. | 1011 Evans Hall
Jan Vecer, Charles University in Prague
This talk connects several basic concepts from probability, statistics and economic theory. We study model prediction in the form of a distributional opinion about a random variable X and show how to test this prediction against alternative views. Different model opinions can be traded on a hypothetical market that trades their differences. Using a utility maximization technique, we describe such a market for any general random variable X and any utility function U. We specify the optimal behavior of agents and the total market that aggregates all available opinions and show that a correct distributional opinion realizes profit in expectation against any other opinion, giving a novel technique for model selection. The expected profit from this trading defines statistical divergence. In particular, exponential utility gives divergence that is very close to Kullback-Leibler and the logarithmic utility gives a novel f-divergence. Analytical solutions are available for random variables from the exponential family. We also determine the distribution corresponding to the aggregated view of all available opinions, giving a novel technique for model averaging.