Learning Parameters by Prediction Markets and Kelly Rule for Graphical Models

Abstract

We consider the case where a large number of human and machine agents collaborate to estimate a joint distribution on events. Some of these agents may be statistical learners processing large volumes of data, but typically any one agent will have access to only some of the data sources. Prediction markets have proven to be an accurate and robust mechanism for aggregating such estimates (Chen and Pennock, 2010), (Barbu and Lay, 2011). Agents in a prediction market trade on futures in events of interest. Their trades collectively determine a probability distribution. Crucially, limited trading resources force agents to prioritize adjustments to the market distribution. Optimally allocating these resources is a challenging problem. In the economic spirit of specialization, we expect prediction markets to do even better if agents can focus on beliefs, and hand off those beliefs to an optimal trading algorithm. Kelly (1956) solved the optimal investment problem for single-asset markets. In previous work, we developed efficient methods to update both the joint probability distribution and user's assets for the graphical model based prediction market (Sun et al., 2012). In this paper we create a Kelly rule automated trader for combinatorial prediction markets and evaluate its performance by numerical simulation.