Bounded-Abstention Multi-horizon Time-series Forecasting

TL;DR

The paper addresses abstention in multi-horizon time-series forecasting by introducing bounded-abstention to preserve the predictive horizon's structure. It develops three abstention settings—full, partial, and interval—and derives optimal selection policies under a coverage constraint, then presents practical learning algorithms (FAbFor, PAbFor, IntAbFor) that jointly learn a forecaster and a conditional risk estimator with a calibrated selection mechanism. Using a two-head network and a $\beta$-NLL loss to estimate per-step risks $\rho_t$ and variances $\hat{\sigma}^2_t$, the authors calibrate thresholds on a hold-out set to satisfy the target coverage $c$, ensuring reliable abstention behavior. Across 24 real-world datasets, interval abstention often achieves the lowest selective risk while adhering to the coverage constraint, significantly outperforming strong baselines and enabling safer, more trustworthy multi-horizon forecasts in high-stakes domains.

Abstract

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.

Figures (4)

• Figure 1: Illustration of possible forecasts when using abstention in a multi-horizon setting. (a) The model offers a forecast for the entire horizon, i.e., the full forecast is accepted. (b) Standard abstention decides independently for each time step whether to accept or abstain from making a prediction, hence the forecast is not guaranteed to be provided for a contiguous time interval. (c) Full abstention only allows rejecting the forecast for the entire horizon. (d) Partial abstention lets the model provide a forecast for part of horizon: the forecast must start from the first time step but it may choose the end time step. (e) Interval abstention offers the most flexibility: it can offer a forecast for any contiguous interval within the horizon, i.e., it can choose any start and end point.
• Figure 2: Each dataset's average selective risk $\hat{\mathcal{R}}$ for all methods across six target coverages in the full abstention setting. For all the coverage level considered, FAbFor consistently achieves a lower selective risk than the baselines in most of the datasets.
• Figure 3: Average selective risk per step for FAbFor, PAbFor, IntAbFor, and Accept-cH across six target coverages on four representative datasets. IntAbFor achieves often the lowest risk by leveraging the highest flexibility, followed by, in order, PAbFor and FAbFor. Accept-cH, which forecasts all time-series until step $cH$, performs worse.
• Figure 4: Constraint satisfaction ($ConSat$) as a function of the tolerance $\epsilon$ for our three strategies and the baselines.

Theorems & Definitions (6)

• Definition 1: Full Abstention
• Theorem 1
• Definition 2: Partial Abstention
• Theorem 2
• Definition 3: Interval Abstention
• Theorem 3