Isoelastic Agents and Wealth Updates in Machine Learning Markets

Recently, prediction markets have shown considerable promise for developing flexible mechanisms for machine learning. In this paper, agents with isoelastic utilities are considered. It is shown that the costs associated with homogeneous markets of agents with isoelastic utilities produce equilibrium prices corresponding to alpha-mixtures, with a particular form of mixing component relating to each agent's wealth. We also demonstrate that wealth accumulation for logarithmic and other isoelastic agents (through payoffs on prediction of training targets) can implement both Bayesian model updates and mixture weight updates by imposing different market payoff structures. An iterative algorithm is given for market equilibrium computation. We demonstrate that inhomogeneous markets of agents with isoelastic utilities outperform state of the art aggregate classifiers such as random forests, as well as single classifiers (neural networks, decision trees) on a number of machine learning benchmarks, and show that isoelastic combination methods are generally better than their logarithmic counterparts.Comment: Appears in Proceedings of the 29th International Conference on Machine Learning (ICML 2012

Information Aggregation in Exponential Family Markets

We consider the design of prediction market mechanisms known as automated market makers. We show that we can design these mechanisms via the mold of \emph{exponential family distributions}, a popular and well-studied probability distribution template used in statistics. We give a full development of this relationship and explore a range of benefits. We draw connections between the information aggregation of market prices and the belief aggregation of learning agents that rely on exponential family distributions. We develop a very natural analysis of the market behavior as well as the price equilibrium under the assumption that the traders exhibit risk aversion according to exponential utility. We also consider similar aspects under alternative models, such as when traders are budget constrained

Predictive Analysis for Social Processes II: Predictability and Warning Analysis

This two-part paper presents a new approach to predictive analysis for social processes. Part I identifies a class of social processes, called positive externality processes, which are both important and difficult to predict, and introduces a multi-scale, stochastic hybrid system modeling framework for these systems. In Part II of the paper we develop a systems theory-based, computationally tractable approach to predictive analysis for these systems. Among other capabilities, this analytic methodology enables assessment of process predictability, identification of measurables which have predictive power, discovery of reliable early indicators for events of interest, and robust, scalable prediction. The potential of the proposed approach is illustrated through case studies involving online markets, social movements, and protest behavior