Quantile-Free Regression: A Flexible Alternative to Quantile Regression

Thomas Pouplin, Alan Jeffares, Nabeel Seedat, Mihaela van der Schaar

Primary Area: probabilistic methods (Bayesian methods, variational inference, sampling, UQ, etc.)

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Keywords: Quantile regression, interval regression, pinball loss, neural networks

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TL;DR: A flexible alternative to quantile regression overcoming the need to prespecify specific quantiles.

Abstract: Constructing valid prediction intervals rather than point estimates is a well-established method for uncertainty quantification in the regression setting. Models equipped with this capacity output an interval of values in which the ground truth target will fall with some prespecified probability. This is an essential requirement in many real-world applications in which simple point predictions' inability to convey the magnitude and frequency of errors renders them insufficient for high-stakes decisions. Quantile regression is well-established as a leading approach for obtaining such intervals via the empirical estimation of quantiles in the (non-parametric) distribution of outputs. This method is simple, computationally inexpensive, interpretable, assumption-free, and highly effective. However, it does require that the quantiles being learned are chosen a priori. This results in either (a) intervals that are arbitrarily symmetric around the median which is sub-optimal for real-world skewed distributions or (b) learning an excessive number of intervals. In this work, we propose Quantile-Free Regression (QFR), a direct replacement for quantile regression which liberates it from this limitation whilst maintaining its strengths. We demonstrate that this added flexibility results in intervals with an improvement in desirable qualities (e.g. sharpness) whilst maintaining the essential coverage guarantees of quantile regression.

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Submission Number: 7548