A tutorial on conformal prediction

Conformal prediction uses past experience to determine precise levels of confidence in new predictions. Given an error probability $\epsilon$, together with a method that makes a prediction $\hat{y}$ of a label $y$, it produces a set of labels, typically containing $\hat{y}$, that also contains $y$ with probability $1-\epsilon$. Conformal prediction can be applied to any method for producing $\hat{y}$: a nearest-neighbor method, a support-vector machine, ridge regression, etc. Conformal prediction is designed for an on-line setting in which labels are predicted successively, each one being revealed before the next is predicted. The most novel and valuable feature of conformal prediction is that if the successive examples are sampled independently from the same distribution, then the successive predictions will be right $1-\epsilon$ of the time, even though they are based on an accumulating dataset rather than on independent datasets. In addition to the model under which successive examples are sampled independently, other on-line compression models can also use conformal prediction. The widely used Gaussian linear model is one of these. This tutorial presents a self-contained account of the theory of conformal prediction and works through several numerical examples. A more comprehensive treatment of the topic is provided in "Algorithmic Learning in a Random World", by Vladimir Vovk, Alex Gammerman, and Glenn Shafer (Springer, 2005).Comment: 58 pages, 9 figure

Discretized conformal prediction for efficient distribution-free inference

In regression problems where there is no known true underlying model, conformal prediction methods enable prediction intervals to be constructed without any assumptions on the distribution of the underlying data, except that the training and test data are assumed to be exchangeable. However, these methods bear a heavy computational cost-and, to be carried out exactly, the regression algorithm would need to be fitted infinitely many times. In practice, the conformal prediction method is run by simply considering only a finite grid of finely spaced values for the response variable. This paper develops discretized conformal prediction algorithms that are guaranteed to cover the target value with the desired probability, and that offer a tradeoff between computational cost and prediction accuracy

Predictive Inference with Feature Conformal Prediction

Conformal prediction is a distribution-free technique for establishing valid prediction intervals. Although conventionally people conduct conformal prediction in the output space, this is not the only possibility. In this paper, we propose feature conformal prediction, which extends the scope of conformal prediction to semantic feature spaces by leveraging the inductive bias of deep representation learning. From a theoretical perspective, we demonstrate that feature conformal prediction provably outperforms regular conformal prediction under mild assumptions. Our approach could be combined with not only vanilla conformal prediction, but also other adaptive conformal prediction methods. Apart from experiments on existing predictive inference benchmarks, we also demonstrate the state-of-the-art performance of the proposed methods on large-scale tasks such as ImageNet classification and Cityscapes image segmentation.The code is available at \url{https://github.com/AlvinWen428/FeatureCP}.Comment: Published as a conference paper at ICLR 202

Conformal Prediction: a Unified Review of Theory and New Challenges

In this work we provide a review of basic ideas and novel developments about Conformal Prediction -- an innovative distribution-free, non-parametric forecasting method, based on minimal assumptions -- that is able to yield in a very straightforward way predictions sets that are valid in a statistical sense also in in the finite sample case. The in-depth discussion provided in the paper covers the theoretical underpinnings of Conformal Prediction, and then proceeds to list the more advanced developments and adaptations of the original idea.Comment: arXiv admin note: text overlap with arXiv:0706.3188, arXiv:1604.04173, arXiv:1709.06233, arXiv:1203.5422 by other author

Criteria of efficiency for conformal prediction

We study optimal conformity measures for various criteria of efficiency of classification in an idealised setting. This leads to an important class of criteria of efficiency that we call probabilistic; it turns out that the most standard criteria of efficiency used in literature on conformal prediction are not probabilistic unless the problem of classification is binary. We consider both unconditional and label-conditional conformal prediction.Comment: 31 page