Uncertainty quantification with conformal prediction

24 Jan 23 00:00 UTC

Uncertainty quantification (UQ) in machine learning is the practice of measuring or estimating uncertainty in models. It is a set of tools to understand the limitations of models and predictions, and to make better decisions. UQ is a key …

An example of conformalization for a regression model. Above, a quantile confidence interval around the prediction has good coverage but at the cost of high width. Below, a conformal quantile regression interval has similar coverage but much smaller width thanks to its adaptivity.

Miguel de Benito Delgado

After several years working as a software developer, Miguel pursued studies in pure mathematics in Madrid and Munich. After finishing his PhD in analysis, and a short research stay in ML, he finally transitioned into the field and ended up working as an applied researcher at the appliedAI Initiative, where he went on to found and head the TransferLab.

Conformal prediction is a method for uncertainty quantification that is based on the idea of conformal sets (CS). A CS is a set of predictions that is guaranteed to contain the true value with a certain probability. This probability is called the confidence level of the CS. The CSs are constructed such that the confidence level is independent of the data distribution and the model’s structure or uncertainty. This means that the CPs are distribution-free and model-agnostic. They are very simple to compute and involve only a calibration step involving quantiles of a so-called conformal score over unseen data.

In this talk we introduce conformal prediction and its applications to classification and regression. We highlight the key assumptions of the method and discuss its main challenges. We also discuss the main differences between conformal prediction and other uncertainty quantification methods.

References

[Ang22C]

Conformal Risk Control, Anastasios N. Angelopoulos, Stephen Bates, Adam Fisch, Lihua Lei, Tal Schuster.

Aug 2022

We extend conformal prediction to control the expected value of any monotone loss function. The algorithm generalizes split conformal prediction together with its coverage guarantee. Like conformal prediction, the conformal risk control procedure is tight up to an $\mathcal{O}(1/n)$ factor. Worked examples from computer vision and natural language processing demonstrate the usage of our algorithm …

[Ang22G]

A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification, Anastasios N. Angelopoulos, Stephen Bates.

Dec 2022

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 …

[Ang22L]

Learn then Test: Calibrating Predictive Algorithms to Achieve Risk Control, Anastasios N. Angelopoulos, Stephen Bates, Emmanuel J. Candès, Michael I. Jordan, Lihua Lei.

Sep 2022

We introduce a framework for calibrating machine learning models so that their predictions satisfy explicit, finite-sample statistical guarantees. Our calibration algorithms work with any underlying model and (unknown) data-generating distribution and do not require model refitting. The framework addresses, among other examples, false discovery rate control in multi-label classification, …

[Bar22C]

Conformal prediction beyond exchangeability, Rina Foygel Barber, Emmanuel J. Candes, Aaditya Ramdas, Ryan J. Tibshirani.

Sep 2022

Conformal prediction is a popular, modern technique for providing valid predictive inference for arbitrary machine learning models. Its validity relies on the assumptions of exchangeability of the data, and symmetry of the given model fitting algorithm as a function of the data. However, exchangeability is often violated when predictive models are deployed in practice. For example, if the data …

Publication

[Bat21D]

Distribution-Free, Risk-Controlling Prediction Sets, Stephen Bates, Anastasios Angelopoulos, Lihua Lei, Jitendra Malik, Michael I. Jordan.

Aug 2021

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 …

[Gib21A]

Adaptive Conformal Inference Under Distribution Shift, Isaac Gibbs, Emmanuel Candes.

2021

We develop methods for forming prediction sets in an online setting where the data generating distribution is allowed to vary over time in an unknown fashion. Our framework builds on ideas from conformal inference to provide a general wrapper that can be combined with any black box method that produces point predictions of the unseen label or estimated quantiles of its distribution. While previous …

Publication

[Gib22C]

Conformal Inference for Online Prediction with Arbitrary Distribution Shifts, Isaac Gibbs, Emmanuel Candès.

Oct 2022

Conformal inference is a powerful tool for quantifying the uncertainty around predictions made by black-box models (e.g. neural nets, random forests). Formally, this methodology guarantees that if the training and test data are exchangeable (e.g. i.i.d.) then we can construct a prediction set $C$ for the target $Y$ such that $P(Y \in C) = 1-\alpha$ for any target level $\alpha$. In this article, …

Publication

[Rom19C]

Conformalized Quantile Regression, Yaniv Romano, Evan Patterson, Emmanuel Candes.

2019

Conformal prediction is a technique for constructing prediction intervals that attain valid coverage in finite samples, without making distributional assumptions. Despite this appeal, existing conformal methods can be unnecessarily conservative because they form intervals of constant or weakly varying length across the input space. In this paper we propose a new method that is fully adaptive to …

Publication

[Stu22L]

Learning Optimal Conformal Classifiers, David Stutz, Krishnamurthy Dj Dvijotham, Ali Taylan Cemgil, Arnaud Doucet.

May 2022

Modern deep learning based classifiers show very high accuracy on test data but this does not provide sufficient guarantees for safe deployment, especially in high-stake AI applications such as medical diagnosis. Usually, predictions are obtained without a reliable uncertainty estimate or a formal guarantee. Conformal prediction (CP) addresses these issues by using the classifier's predictions, …

Publication

[Vov05A]

Algorithmic Learning in a Random World, Vladimir Vovk, Alexander Gammerman, Glenn Shafer.

Mar 2005

Publication

[Vov12C]

Conditional Validity of Inductive Conformal Predictors, Vladimir Vovk.

Nov 2012

Conformal predictors are set predictors that are automatically valid in the sense of having coverage probability equal to or exceeding a given confidence level. Inductive conformal predictors are a computationally efficient version of conformal predictors satisfying the same property of validity. However, inductive conformal predictors have been only known to control unconditional coverage …

Publication

References

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