Design and Analysis of a Synthetic Prediction Market using Dynamic Convex Sets
This work provides a novel approach to function approximation and data distribution modeling for researchers interested in alternative computational paradigms, offering an incremental contribution to the field.
This paper introduces a synthetic prediction market where agent purchase logic is based on a sigmoid transformation of a convex semi-algebraic set. The market, using a logarithmic scoring rule, can arbitrarily closely approximate a binary function on input data under specific geometric assumptions, and the authors demonstrate its ability to model data distributions using an evolutionary algorithm.
We present a synthetic prediction market whose agent purchase logic is defined using a sigmoid transformation of a convex semi-algebraic set defined in feature space. Asset prices are determined by a logarithmic scoring market rule. Time varying asset prices affect the structure of the semi-algebraic sets leading to time-varying agent purchase rules. We show that under certain assumptions on the underlying geometry, the resulting synthetic prediction market can be used to arbitrarily closely approximate a binary function defined on a set of input data. We also provide sufficient conditions for market convergence and show that under certain instances markets can exhibit limit cycles in asset spot price. We provide an evolutionary algorithm for training agent parameters to allow a market to model the distribution of a given data set and illustrate the market approximation using two open source data sets. Results are compared to standard machine learning methods.