Marginally Useful: An Information-Gap Identity in Split Conformal Prediction

Battle Count: 73

The paper is highly relevant to quantitative trading in that it formalizes a critical limitation of conformal prediction in financial settings with stochastic volatility (heteroscedasticity). The Kelly betting interpretation directly connects to trading strategy evaluation. The paper warns that residual pooling (the standard conformal approach) imposes a permanent log-score penalty equal to I(R;X), which in finance corresponds to ignoring conditional volatility structure. However, the paper is theoretical and does not propose a specific trading strategy or empirical backtest. It is most relevant to practitioners who use conformal prediction for risk bounds or prediction intervals in financial forecasting.

This is a theoretical/mathematical note with no complex implementation. The key result (Proposition 1) is a one-line identity derived from the chain rule for KL divergence. The illustrative figures use simple synthetic heteroscedastic data. The practical implication (using normalized scores s(x,y) = |y-μ̂(x)|/σ̂(x)) is straightforward to implement.

The paper provides code, figures, and an interactive companion at https://conformalprediction.net and https://github.com/microprediction/conformal_prediction. The theoretical results are fully derivable from the proofs provided. However, as a theoretical note, there are no empirical experiments to reproduce beyond the illustrative figures.