From Samples to Scenarios: A New Paradigm for Probabilistic Forecasting

2025-09-24

AI Summary

Existing probabilistic time series forecasting relies on Monte Carlo sampling, suffering from ill-defined probabilistic interpretations, low coverage rates, and high computational overhead. To address these limitations, this paper introduces the “probabilistic scenario” paradigm—a sampling-free approach that directly models a finite set of scenario-probability pairs. Instead of approximating distributions via sampling, the method jointly learns high-confidence scenarios alongside their exact probability masses. We propose TimePrism, an extremely lightweight architecture comprising only three parallel linear layers, which produces scenarios and their associated probabilities in an end-to-end manner. Evaluated on five standard benchmarks, TimePrism achieves state-of-the-art performance on 9 out of 10 sub-tasks across two core metrics. It significantly improves prediction coverage, interpretability, and computational efficiency, thereby validating both the effectiveness and broad applicability of the probabilistic scenario paradigm.

Technology Category

• Reasoning under Uncertainty: Probabilistic Programming
• Machine Learning: Probabilistic Circuits and Graphical Models
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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 extbf{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 extbf{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.

Problem

• Addressing limitations of sampling-based probabilistic time series forecasting
• Providing explicit scenario-probability pairs instead of Monte Carlo approximation
• Reframing forecasting to learn plausible scenarios with corresponding probabilities

Innovation

• Introduces Probabilistic Scenarios paradigm for forecasting
• Proposes TimePrism model with three parallel linear layers
• Learns finite Scenario-Probability pairs instead of sampling