From Samples to Scenarios: A New Paradigm for Probabilistic Forecasting

TL;DR

This work introduces the Probabilistic Scenarios paradigm, an alternative paradigm designed to address the limitations of sampling that operates by directly producing a finite set of scenario, Probability pairs, thus avoiding Monte Carlo-like approximation.

Abstract

Most state-of-the-art probabilistic time series forecasting models rely on sampling to represent future uncertainty. However, this paradigm suffers from inherent limitations, such as lacking explicit probabilities, inadequate coverage, and high computational costs. In this work, we introduce \textbf{Probabilistic Scenarios}, an alternative paradigm designed to address the limitations of sampling. It operates by directly producing a finite set of \{Scenario, Probability\} pairs, thus avoiding Monte Carlo-like approximation. To validate this paradigm, we propose \textbf{TimePrism}, a simple model composed of only three parallel linear layers. Surprisingly, TimePrism achieves 9 out of 10 state-of-the-art results across five benchmark datasets on two metrics. The effectiveness of our paradigm comes from a fundamental reframing of the learning objective. Instead of modeling an entire continuous probability space, the model learns to represent a set of plausible scenarios and corresponding probabilities. Our work demonstrates the potential of the Probabilistic Scenarios paradigm, opening a promising research direction in forecasting beyond sampling.

Figures (8)

• Figure 1: Motivation, solution, and evaluation of this work. We illustrate the limitations of the prevailing sampling-based paradigm for probabilistic forecasting. In response, we introduce Probabilistic Scenarios, a new paradigm that directly produces a set of {Scenario, Probability} pairs, and validate its potential with a simple proof-of-concept model, TimePrism.
• Figure 2: Probabilistic Scenarios Paradigm and Unified Evaluation Framework. The left panel illustrates an ideal behavior: a model trained on a dataset where similar histories lead to diverse futures should learn to output {Scenario, Probability} pairs that reflect the empirical frequency of those futures. The right panel details our evaluation framework, which links the limitations of sampling to adapted metrics and provides distinct yet comparable formulations for both paradigms.
• Figure 3: Structure of TimePrism, a linear model to demonstrate the potential of the Probabilistic Scenarios paradigm. The model operates in three parallel streams: after an initial decomposition, separate linear layers generate a basis of $M$ trend and $K$ seasonal forecasts. Simultaneously, a third linear layer produces the $N=M*K$ logits from the undecomposed history. This architecture, built within the Probabilistic Scenarios paradigm, achieves competitive performance despite its simplicity, demonstrating the potential of the new paradigm.
• Figure 4: Qualitative Analysis of the New Paradigm. A visual comparison between the Probabilistic Scenarios paradigm (TimePrism) and the Sampling Paradigm (TACTiS-2). The figure highlights their distinct behaviors in both common high-peak cases and a rare low-peak case, on the Solar dataset.
• Figure 5: Calibration Diagnostics. The diagnostics show different behaviors across datasets: (a)(b) Exchange dataset demonstrates near-perfect calibration; (c)(d) Solar dataset exhibits a slightly conservative profile to ensure robust tail coverage.