Improving the statistical efficiency of cross-conformal prediction

Vovk (2015) introduced cross-conformal prediction, a modification of split conformal designed to improve the width of prediction sets. The method, when trained with a miscoverage rate equal to $\alpha$ and $n \gg K$, ensures a marginal coverage of at least $1 - 2\alpha - 2(1-\alpha)(K-1)/(n+K)$, where $n$ is the number of observations and $K$ denotes the number of folds. A simple modification of the method achieves coverage of at least $1-2\alpha$. In this work, we propose new variants of both methods that yield smaller prediction sets without compromising the latter theoretical guarantee. The proposed methods are based on recent results deriving more statistically efficient combination of p-values that leverage exchangeability and randomization. Simulations confirm the theoretical findings and bring out some important tradeoffs.

Conformal online model aggregation

Conformal prediction equips machine learning models with a reasonable notion of uncertainty quantification without making strong distributional assumptions. It wraps around any black-box prediction model and converts point predictions into set predictions that have a predefined marginal coverage guarantee. However, conformal prediction only works if we fix the underlying machine learning model in advance. A relatively unaddressed issue in conformal prediction is that of model selection and/or aggregation: for a given problem, which of the plethora of prediction methods (random forests, neural nets, regularized linear models, etc.) should we conformalize? This paper proposes a new approach towards conformal model aggregation in online settings that is based on combining the prediction sets from several algorithms by voting, where weights on the models are adapted over time based on past performance.