Exact and Approximate Conformal Inference for Multi-task Learning
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-task learning within a regression setting, 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-task predictors while preserving computational advantages. We also provide both theoretical and empirical evidence of the effectiveness of these methods.
Submission Length: Long submission (more than 12 pages of main content)
Assigned Action Editor: ~Trevor_Campbell1
Submission Number: 1451
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