# Discriminative Learning of Prediction Intervals

arXiv: https://arxiv.org/abs/1710.05888 · HTML: https://mlsanity.com/paper/1710.05888/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Oct 2017.

## Built on by (most cited first, 5 of 5)

- [A Survey on Uncertainty Quantification Methods for Deep Learning](https://mlsanity.com/paper/2302.13425/) (2023)
- [Learning Prediction Intervals for Regression: Generalization and Calibration](https://mlsanity.com/paper/2102.13625/) (2021)
- [Quantifying Epistemic Uncertainty in Deep Learning](https://mlsanity.com/paper/2110.12122/) (2021)
- [Efficient Uncertainty Quantification and Reduction for Over-Parameterized Neural Networks](https://mlsanity.com/paper/2306.05674/) (2023)
- [Exploring Uncertainty in Deep Learning for Construction of Prediction Intervals](https://mlsanity.com/paper/2104.12953/) (2021)

## Abstract (arXiv)

In this work we consider the task of constructing prediction intervals in an inductive batch setting. We present a discriminative learning framework which optimizes the expected error rate under a budget constraint on the interval sizes. Most current methods for constructing prediction intervals offer guarantees for a single new test point. Applying these methods to multiple test points can result in a high computational overhead and degraded statistical guarantees. By focusing on expected errors, our method allows for variability in the per-example conditional error rates. As we demonstrate both analytically and empirically, this flexibility can increase the overall accuracy, or alternatively, reduce the average interval size. While the problem we consider is of a regressive flavor, the loss we use is combinatorial. This allows us to provide PAC-style, finite-sample guarantees. Computationally, we show that our original objective is NP-hard, and suggest a tractable convex surrogate. We conclude with a series of experimental evaluations.