TimeGMM: Single-Pass Probabilistic Forecasting via Adaptive Gaussian Mixture Models with Reversible Normalization

2026-01-18

AI Summary

This work proposes TimeGMM, a novel framework for probabilistic time series forecasting that overcomes limitations of existing methods—such as reliance on computationally expensive sampling or restrictive parametric assumptions—by efficiently modeling complex, arbitrary-shaped predictive distributions through a Gaussian Mixture Model (GMM) in a single forward pass. To address temporal–probabilistic distribution shifts, TimeGMM introduces GMM-adaptive Reversible Instance Normalization (GRIN), which dynamically corrects such misalignments. The framework further incorporates a Conditional Temporal-Probabilistic Decoder (CTPD) and a dedicated Temporal Encoder (TE) to jointly learn temporal dependencies and GMM parameters. Experimental results demonstrate that TimeGMM achieves significant improvements over state-of-the-art approaches, with relative gains of up to 22.48% in CRPS and 21.23% in NMAE.

Technology Category

• Machine Learning: Time-Series/Data Streams
• Reasoning under Uncertainty: Relational Probabilistic Models
• Planning, Routing, and Scheduling: Temporal Planning

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

Probabilistic time series forecasting is crucial for quantifying future uncertainty, with significant applications in fields such as energy and finance. However, existing methods often rely on computationally expensive sampling or restrictive parametric assumptions to characterize future distributions, which limits predictive performance and introduces distributional mismatch. To address these challenges, this paper presents TimeGMM, a novel probabilistic forecasting framework based on Gaussian Mixture Models (GMM) that captures complex future distributions in a single forward pass. A key component is GMM-adapted Reversible Instance Normalization (GRIN), a novel module designed to dynamically adapt to temporal-probabilistic distribution shifts. The framework integrates a dedicated Temporal Encoder (TE-Module) with a Conditional Temporal-Probabilistic Decoder (CTPD-Module) to jointly capture temporal dependencies and mixture distribution parameters. Extensive experiments demonstrate that TimeGMM consistently outperforms state-of-the-art methods, achieving maximum improvements of 22.48\% in CRPS and 21.23\% in NMAE.

Problem

• probabilistic forecasting
• time series
• distribution mismatch
• Gaussian Mixture Models
• temporal dependencies

Innovation

• Gaussian Mixture Models
• Reversible Instance Normalization
• Probabilistic Forecasting
• Single-Pass Inference
• Temporal-Probabilistic Modeling