Title: Dynamic scoring: Probabilistic model selection based on utility maximization
Authors: Jan Vecer - Charles University, MFF (Czech Republic) [presenting]
Abstract: A novel and general approach of model selection is proposed for probability estimates that can also be applied in the time evolving setting. The basic idea is that any discrepancy between two different probability estimates opens a possibility to compare them by setting a trade on a hypothetical betting market that trades probabilities. The mechanism of this market and the behavior of agents in this market is described. An agent maximizing some utility function determines the optimal bet size for given odds. This procedure produces supply and demand functions, the size of the bet as a function of a trading probability. These functions are analytical for the choice of logarithmic and exponential utility functions. Having two probability estimates and the corresponding supply and demand functions, the trade matching these two estimates happens at the resulting equilibrium at the intersection of the supply and demand functions. It is shown that an agent using true probabilities will realize a profit when trading against any other set of probabilities.