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

Lei Liu, Tengyuan Liu, Hongwei Zhao, Jiahui Huang, Ruibo Guo, Bin Li

TL;DR

This work tackles probabilistic time series forecasting by eliminating repeated sampling and strong distributional priors. It introduces TimeGMM, a single-pass framework that represents future outcomes with Gaussian Mixture Models and uses a novel GMM-adapted Reversible Instance Normalization (GRIN) to adapt to distribution shifts, integrated with a Temporal Encoder and a Conditional Temporal-Probabilistic Decoder. The method jointly learns temporal dependencies and GMM parameters, optimized via a negative log-likelihood objective plus auxiliary loss terms, with weights denormalized through GRIN during decoding. Empirical results on the ProbTS benchmark show TimeGMM consistently outperforms state-of-the-art methods in CRPS and NMAE, with ablations confirming the importance of both GMM modeling and GRIN normalization for accuracy and robustness.

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.

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

TL;DR

This work tackles probabilistic time series forecasting by eliminating repeated sampling and strong distributional priors. It introduces TimeGMM, a single-pass framework that represents future outcomes with Gaussian Mixture Models and uses a novel GMM-adapted Reversible Instance Normalization (GRIN) to adapt to distribution shifts, integrated with a Temporal Encoder and a Conditional Temporal-Probabilistic Decoder. The method jointly learns temporal dependencies and GMM parameters, optimized via a negative log-likelihood objective plus auxiliary loss terms, with weights denormalized through GRIN during decoding. Empirical results on the ProbTS benchmark show TimeGMM consistently outperforms state-of-the-art methods in CRPS and NMAE, with ablations confirming the importance of both GMM modeling and GRIN normalization for accuracy and robustness.

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.
Paper Structure (11 sections, 14 equations, 2 figures, 3 tables)

This paper contains 11 sections, 14 equations, 2 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Methodology
  3. Distribution-Adaptive Transform
  4. Temporal Encoder (TE)
  5. Conditional Temporal-Probabilistic Decoder (CTPD)
  6. GMM Optimize
  7. Experiments
  8. Experiment Settings
  9. Main Results
  10. Ablation Study
  11. Conclusion

Figures (2)

  • Figure 1: A comparison between the traditional methods and the proposed method.
  • Figure 2: The overall framework of the proposed TimeGMM. Part A performs adaptive normalization and trend-seasonal decomposition; Part B captures temporal patterns, extracting and encoding historical information; Part C decodes encoder outputs into GMM parameters for probabilistic forecasting; Part D constructs the probability distribution from GMM parameters and computes the loss using negative log-likelihood, expected L2 error, and weight constraints.