Asymmetric Peak-Aware Loss for Peak-Critical Time Series Forecasting

2026-07-16

AI Summary

This work addresses the tendency of conventional time series forecasting models to underestimate critical peaks due to their reliance on symmetric loss functions, which can lead to high-risk outcomes. To mitigate this issue, the authors propose a model-agnostic Asymmetric Peak-Aware Loss (APAL) that intensifies penalties for underestimation and dynamically assigns higher weights to peak regions, thereby enhancing the model’s ability to accurately predict salient peaks. Additionally, a tailored evaluation protocol is introduced to assess both tail error and temporal precision of peak predictions. Experimental results across multiple real-world datasets—including pedestrian flow—demonstrate that APAL significantly improves tail prediction accuracy and peak detection performance, as measured by F1 score and timing error, while maintaining overall prediction error within acceptable bounds through an effective trade-off.

Abstract

In many operational time-series forecasting applications, such as crowd demand forecasting, the risk related to under-prediction is substantially higher than that of over-prediction. Accurate prediction of rare demand spikes plays a critical role in downstream tasks. Yet most time-series forecasters are trained with symmetric objectives (e.g., MSE, MAE) and evaluated primarily on aggregate error, which can mask failures in extreme-values and peak-timing predictions. We introduce Asymmetric Peak-Aware Loss (APAL), a simple, model-agnostic objective that (i) penalizes under-predictions more heavily and (ii) increases the training weight of peak regions within each forecast window. We further propose a peak-critical evaluation protocol that complements MAE/MSE with channel-wise tail error (Top-10% and Top-1%) and peak metrics (precision, recall, F1 under timing tolerance, and peak timing error). We evaluate APAL on long-horizon multivariate forecasting across five state-of-the-art backbones, with a focus on pedestrian demand forecasting using (i) a production-ready subset of the City of Melbourne pedestrian hourly count dataset and (ii) a beach visitor count dataset. The generality of the loss function for time-series forecasting is tested on additional benchmarks. Across peak-critical datasets and settings, APAL improves tail accuracy and peak-prediction quality while exposing a controllable trade-off with aggregate error, making it a practical solution when peak-prediction failures are the dominant operational concern.

Problem

• asymmetric loss
• peak prediction
• time series forecasting
• tail error
• demand spikes

Innovation

• Asymmetric Loss
• Peak-Aware Forecasting
• Time Series Prediction
• Tail Error
• Model-Agnostic Objective