# Bounded-Abstention Multi-horizon Time-series Forecasting

arXiv: https://arxiv.org/abs/2602.04714 · HTML: https://mlsanity.com/paper/2602.04714/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 42 references that are in the map.
- First posted on arXiv 4 Feb 2026.

## Builds on (most cited first, 24 of 24)

- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [Selective Classification for Deep Neural Networks](https://mlsanity.com/paper/1705.08500/) (2017)
- [The UCR Time Series Archive](https://mlsanity.com/paper/1810.07758/) (2018)
- [SelectiveNet: A Deep Neural Network with an Integrated Reject Option](https://mlsanity.com/paper/1901.09192/) (2019)
- [WeatherBench: A benchmark dataset for data-driven weather forecasting](https://mlsanity.com/paper/2002.00469/) (2020)
- [A Multi-Horizon Quantile Recurrent Forecaster](https://mlsanity.com/paper/1711.11053/) (2017)
- [A Theoretically Grounded Application of Dropout in Recurrent Neural Networks](https://mlsanity.com/paper/1512.05287/) (2015)
- [On the Pitfalls of Heteroscedastic Uncertainty Estimation with Probabilistic Neural Networks](https://mlsanity.com/paper/2203.09168/) (2022)
- [Machine Learning with a Reject Option: A survey](https://mlsanity.com/paper/2107.11277/) (2021)
- [Sequential Predictive Conformal Inference for Time Series](https://mlsanity.com/paper/2212.03463/) (2022)
- [Optimal strategies for reject option classifiers](https://mlsanity.com/paper/2101.12523/) (2021)
- [ClimateLearn: Benchmarking Machine Learning for Weather and Climate Modeling](https://mlsanity.com/paper/2307.01909/) (2023)
- [Conformal Prediction for Time Series with Modern Hopfield Networks](https://mlsanity.com/paper/2303.12783/) (2023)
- [Bayesian Recurrent Neural Networks](https://mlsanity.com/paper/1704.02798/) (2017)
- [Regression with reject option and application to kNN](https://mlsanity.com/paper/2006.16597/) (2020)
- [SubseasonalClimateUSA: A Dataset for Subseasonal Forecasting and Benchmarking](https://mlsanity.com/paper/2109.10399/) (2021)
- [Frequentist Uncertainty in Recurrent Neural Networks via Blockwise Influence Functions](https://mlsanity.com/paper/2006.13707/) (2020)
- [AUC-based Selective Classification](https://mlsanity.com/paper/2210.10703/) (2022)
- [Deep Neural Network Benchmarks for Selective Classification](https://mlsanity.com/paper/2401.12708/) (2024)
- [Classifiers With a Reject Option for Early Time-Series Classification](https://mlsanity.com/paper/1312.3989/) (2013)
- [Unsupervised Anomaly Detection with Rejection](https://mlsanity.com/paper/2305.13189/) (2023)
- [Forecasting the future development in quality and value of professional football players](https://mlsanity.com/paper/2502.07528/) (2025)
- [Knowing What You Cannot Explain: Learning to Reject Low-Quality Explanations](https://mlsanity.com/paper/2507.12900/) (2025)

## Abstract (arXiv)

Multi-horizon time-series forecasting involves simultaneously making predictions for a consecutive sequence of subsequent time steps. This task arises in many application domains, such as healthcare and finance, where mispredictions can have a high cost and reduce trust. The learning with abstention framework tackles these problems by allowing a model to abstain from offering a prediction when it is at an elevated risk of making a misprediction. Unfortunately, existing abstention strategies are ill-suited for the multi-horizon setting: they target problems where a model offers a single prediction for each instance. Hence, they ignore the structured and correlated nature of the predictions offered by a multi-horizon forecaster. We formalize the problem of learning with abstention for multi-horizon forecasting setting and show that its structured nature admits a richer set of abstention problems. Concretely, we propose three natural notions of how a model could abstain for multi-horizon forecasting. We theoretically analyze each problem to derive the optimal abstention strategy and propose an algorithm that implements it. Extensive evaluation on 24 datasets shows that our proposed algorithms significantly outperforms existing baselines.