Topological Compression of Prediction Market Belief States for Event Forecasting
Aadit Jerfy
Abstract
Topological Data Analysis (TDA) and Persistent Homology (PH) have been utilized in numerous fields$-$from protein modeling to financial analysis$-$to understand the underlying structure of data. In this paper, we incorporate TDA and PH into forecasting models over a prediction market universe to determine whether the belief state of such markets forms an underlying structure whose shape can provide predictive insight. We conclude that single-parameter PH is able to improve predictive ability and calibrated accuracy of linear forecasting models, while two-parameter multipersistence produces similar benefits for nonlinear models.
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