A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification

Black-box machine learning learning methods are now routinely used in high-risk settings, like medical diagnostics, which demand uncertainty quantification to avoid consequential model failures. Distribution-free uncertainty quantification (distribution-free UQ) is a user-friendly paradigm for creating statistically rigorous confidence intervals/sets for such predictions. Critically, the intervals/sets are valid without distributional assumptions or model assumptions, possessing explicit guarantees even with finitely many datapoints. Moreover, they adapt to the difficulty of the input; when the input example is difficult, the uncertainty intervals/sets are large, signaling that the model might be wrong. Without much work and without retraining, one can use distribution-free methods on any underlying algorithm, such as a neural network, to produce confidence sets guaranteed to contain the ground truth with a user-specified probability, such as 90%. Indeed, the methods are easy-to-understand and general, applying to many modern prediction problems arising in the fields of computer vision, natural language processing, deep reinforcement learning, and so on. This hands-on introduction is aimed at a reader interested in the practical implementation of distribution-free UQ who is not necessarily a statistician. We lead the reader through the practical theory and applications of distribution-free UQ, beginning with conformal prediction and culminating with distribution-free control of any risk, such as the false-discovery rate, false positive rate of out-of-distribution detection, and so on. We will include many explanatory illustrations, examples, and code samples in Python, with PyTorch syntax. The goal is to provide the reader a working understanding of distribution-free UQ, allowing them to put confidence intervals on their algorithms, with one self-contained document.