EVEREST: An Evidential, Tail-Aware Transformer for Rare-Event Time-Series Forecasting

TL;DR

EVEREST tackles the challenge of forecasting rare events in multivariate time series by delivering calibrated, tail-aware predictions with a compact transformer. It achieves this through a single-query attention bottleneck plus training-time auxiliaries: an evidential Normal–Inverse–Gamma head for closed-form uncertainty, an EVT tail head using a Generalised Pareto distribution, and a precursor head for early-event supervision, all regularised by a composite loss. The approach yields state-of-the-art True Skill Statistics on SHARP–GOES solar-flare tasks, strong reliability (low Expected Calibration Error), and successful cross-domain transfer to SKAB, all with a small footprint suitable for commodity hardware. Practically, EVEREST provides interpretable attention-based cues, threshold analysis under asymmetric costs, and prospective case-study validation, making it well-suited for high-stakes domains such as space weather, industrial monitoring, and satellite diagnostics. The work demonstrates that coupling a lightweight global aggregator with training-time tail and calibration regularisers can deliver robust, tail-sensitive forecasts without inference overhead.

Abstract

Forecasting rare events in multivariate time-series data is challenging due to severe class imbalance, long-range dependencies, and distributional uncertainty. We introduce EVEREST, a transformer-based architecture for probabilistic rare-event forecasting that delivers calibrated predictions and tail-aware risk estimation, with auxiliary interpretability via attention-based signal attribution. EVEREST integrates four components: (i) a learnable attention bottleneck for soft aggregation of temporal dynamics; (ii) an evidential head for estimating aleatoric and epistemic uncertainty via a Normal--Inverse--Gamma distribution; (iii) an extreme-value head that models tail risk using a Generalized Pareto Distribution; and (iv) a lightweight precursor head for early-event detection. These modules are jointly optimized with a composite loss (focal loss, evidential NLL, and a tail-sensitive EVT penalty) and act only at training time; deployment uses a single classification head with no inference overhead (approximately 0.81M parameters). On a decade of space-weather data, EVEREST achieves state-of-the-art True Skill Statistic (TSS) of 0.973/0.970/0.966 at 24/48/72-hour horizons for C-class flares. The model is compact, efficient to train on commodity hardware, and applicable to high-stakes domains such as industrial monitoring, weather, and satellite diagnostics. Limitations include reliance on fixed-length inputs and exclusion of image-based modalities, motivating future extensions to streaming and multimodal forecasting.

Figures (11)

• Figure 1: Cost--loss analysis for the M5--72 h model under asymmetric costs ($C_{\mathrm{FN}}{:}C_{\mathrm{FP}}=20{:}1$). The left panel shows the cost curve; the right panel highlights the minimum-cost threshold $\tau^\star=0.240$ versus the balanced-score threshold $\tau=0.460$.
• Figure 2: Central–meridian–distance (CMD) quality mask applied to an HMI synoptic magnetogram. The bright-green curve marks the acceptance limit $|\mathrm{CMD}|=70^\circ$; grey wedges beyond this boundary are discarded. Active-region boxes are color-coded by the centroid rule: green outlines (e.g., AR 12263, 12266) fall inside the limit and are retained, whereas red outlines (e.g., AR 12267) lie outside and are excluded. The mask removes limb data affected by foreshortening and line-of-sight artifacts while preserving the central disk used for training and evaluation.
• Figure 3: Reliability diagram for the M5--72 h task. Shaded region shows 95% bootstrap confidence intervals; the dashed line indicates perfect calibration. ECE $=0.016$ with maximum bin gap 0.263.
• Figure 4: Class-conditional calibration for M5--72 h. Left: negative-class reliability curve (ECE = 0.0097). Right: positive-class reliability curve (ECE = 0.4236). Higher positive-class ECE reflects the extreme rarity of M5 events, but the curve remains monotone and near-diagonal at high predicted probabilities.
• Figure 5: High-confidence calibration ($\hat{p}>0.8$) on M5--72 h. Left: observed vs. predicted frequencies for all high-confidence samples (all eight are true flares). Right: histogram of predicted probabilities in this regime. Despite the small sample size, the high-alert region exhibits perfect precision, indicating reliable operational behaviour.