Topological Compression of Prediction Market Belief States for Event Forecasting

Paper: arXiv 2610.25756

Authors: 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.

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 8.0/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper demonstrates high mathematical complexity through its application of Topological Data Analysis and Persistent Homology, combined with robust empirical testing on prediction market data. The novel integration of TDA/PH for forecasting in this domain is a significant strength, supported by a clear methodology and promising results.

Research Flowchart

  flowchart TD
    A[Research Goal: Predictive Insight from Market Belief State Shape] --> B(Methodology: TDA & Persistent Homology Application)
    B --> C{Data/Inputs: Prediction Market Belief States}
    C --> D[Computational Processes: Single-parameter PH & Multi-parameter PH]
    D --> E{Outcome 1: Single-parameter PH improves Linear Model Prediction & Accuracy}
    D --> F{Outcome 2: Multi-parameter PH improves Non-linear Model Prediction & Accuracy}