Calibrated Multiple-Output Quantile Regression with Representation Learning
Authors: Shai Feldman, Stephen Bates, Yaniv Romano; Journal of Machine Learning Research, 24(24):1−48, 2023.
Abstract
We present a novel method for generating predictive regions that encompass a multivariate response variable with a specified probability. Our approach consists of two main components. Firstly, we utilize a deep generative model to learn a representation of the response that follows a unimodal distribution. This learned representation is then subjected to existing multiple-output quantile regression techniques, which are highly effective in such scenarios. The resulting solution is then transformed back to the original response space, resulting in a flexible and informative region with an arbitrary shape, a property lacking in current methods. Secondly, we extend the concept of conformal prediction to the multivariate response setting, allowing us to modify any method to produce sets with a predetermined coverage level. The desired coverage is guaranteed in the finite-sample case for any distribution. Experimental results on both real and synthetic data demonstrate that our method constructs significantly smaller regions compared to existing techniques.
[Abstract]