Distribution-Free, Risk-Controlling Prediction Sets

Abstract

While improving prediction accuracy has been the focus of machine learning in recent years, this alone does not suffice for reliable decision-making. Deploying learning systems in consequential settings also requires calibrating and communicating the uncertainty of predictions. To convey instance-wise uncertainty for prediction tasks, we show how to generate set-valued predictions from a black-box predictor that control the expected loss on future test points at a user-specified level. Our approach provides explicit finite-sample guarantees for any dataset by using a holdout set to calibrate the size of the prediction sets. This framework enables simple, distribution-free, rigorous error control for many tasks, and we demonstrate it in five large-scale machine learning problems: (1) classification problems where some mistakes are more costly than others; (2) multi-label classification, where each observation has multiple associated labels; (3) classification problems where the labels have a hierarchical structure; (4) image segmentation, where we wish to predict a set of pixels containing an object of interest; and (5) protein structure prediction. Lastly, we discuss extensions to uncertainty quantification for ranking, metric learning and distributionally robust learning. * equal contribution see project website at angelopoulos.ai/blog/posts/rcps/

Learn then Test: Calibrating Predictive Algorithms to Achieve Risk Control

“…Most closely related to the present work is the technique of Risk-Controlling Prediction Sets [2] which extends tolerance regions and conformal prediction to give prediction sets that control other notions of statistical error. The present work goes beyond that work to consider prediction with risk control more generally, without restricting the scope to confidence sets.…”

“…Eventually, we will select an element λ ∈ Λ to deploy in our predictions. Unlike [2], our method allows Λ to be multidimensional, we require no special structure of T λ , and Λ can have more than one element. In practice, there will often be structure on Λ, and so we also design multiple testing methods to leverage various kinds of structure for improved power.…”

“…Theorem 1 reduces the problem of risk control into two subproblems: first, generating a p-value for each hypothesis, and second, combining the hypotheses to discover the largest set that controls the risk at level α. To generate p-values, we leverage the hybridized Hoeffding-Bentkus bound from [2]. This solves the first subproblem.…”

“…Note that these examples are uniquely possible using our method, when compared to existing literature, because all previous work in distribution-free uncertainty quantification, such as conformal prediction [1] and risk-controlling prediction sets [2], have required that the risk function be monotonic in λ. We do not make this assumption, and therefore we can simultaneously control many arbitrary risks.…”

Learning from learning machines: a new generation of AI technology to meet the needs of science

“…These may then be put into industrial pipelines optimized to deliver business value, and they can be continuously improved with new data as they are deployed. Conformal prediction techniques now make it possible to obtain accurate prediction intervals (measures of uncertainty) in such settings under only the assumption of access to statistically exchangeable observations [11]. In this case, where we only need to know what an AI model f has learned from data, it is often sufficient to access and analyze f in a black-box manner, and it is often accepted that this model is completely non-understandable-neither explainable nor interpretable.…”