Exact and Approximate Conformal Inference for Multi-Output Regression

• URL: http://arxiv.org/abs/2210.17405v2
• Date: Sat, 22 Jun 2024 20:56:19 GMT
• Title: Exact and Approximate Conformal Inference for Multi-Output Regression
• Authors: Chancellor Johnstone, Eugene Ndiaye,
• Abstract summary: Conformal inference is used in machine learning to quantify uncertainty associated with predictions. In this paper, we explore multi-output regression, delivering exact derivations of conformal inference $p$-values. We also provide both theoretical and empirical evidence of the effectiveness of these methods using both real-world and simulated data.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: It is common in machine learning to estimate a response $y$ given covariate information $x$. However, these predictions alone do not quantify any uncertainty associated with said predictions. One way to overcome this deficiency is with conformal inference methods, which construct a set containing the unobserved response $y$ with a prescribed probability. Unfortunately, even with a one-dimensional response, conformal inference is computationally expensive despite recent encouraging advances. In this paper, we explore multi-output regression, delivering exact derivations of conformal inference $p$-values when the predictive model can be described as a linear function of $y$. Additionally, we propose \texttt{unionCP} and a multivariate extension of \texttt{rootCP} as efficient ways of approximating the conformal prediction region for a wide array of multi-output predictors, both linear and nonlinear, while preserving computational advantages. We also provide both theoretical and empirical evidence of the effectiveness of these methods using both real-world and simulated data.

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