Conditionally Whitened Generative Models for Probabilistic Time Series Forecasting

2025-09-25

AI Summary

Probabilistic forecasting of multivariate time series faces three core challenges: non-stationarity, difficulty in modeling inter-variable dependencies, and distributional shift. To address these, we propose Conditional Whitening Generative Framework (CW-Gen), the first approach to incorporate conditional whitening into diffusion and flow-matching models. CW-Gen leverages structural priors—including dynamic mean estimation and sliding-window covariance—to enhance generative fidelity. We theoretically derive the optimal terminal distribution condition and design a Joint Mean-Covariance Estimator (JMCE) for simultaneous learning of both components. Based on this, we instantiate two novel architectures: CW-Diff and CW-Flow. Extensive experiments across five real-world datasets demonstrate that CW-Gen consistently outperforms six state-of-the-art generative baselines, achieving superior accuracy in capturing non-stationary dynamics and cross-variable dependencies while effectively mitigating distributional shift.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Computer Vision: Diffusion Models for Vision
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Web data generation and simulation
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

Probabilistic forecasting of multivariate time series is challenging due to non-stationarity, inter-variable dependencies, and distribution shifts. While recent diffusion and flow matching models have shown promise, they often ignore informative priors such as conditional means and covariances. In this work, we propose Conditionally Whitened Generative Models (CW-Gen), a framework that incorporates prior information through conditional whitening. Theoretically, we establish sufficient conditions under which replacing the traditional terminal distribution of diffusion models, namely the standard multivariate normal, with a multivariate normal distribution parameterized by estimators of the conditional mean and covariance improves sample quality. Guided by this analysis, we design a novel Joint Mean-Covariance Estimator (JMCE) that simultaneously learns the conditional mean and sliding-window covariance. Building on JMCE, we introduce Conditionally Whitened Diffusion Models (CW-Diff) and extend them to Conditionally Whitened Flow Matching (CW-Flow). Experiments on five real-world datasets with six state-of-the-art generative models demonstrate that CW-Gen consistently enhances predictive performance, capturing non-stationary dynamics and inter-variable correlations more effectively than prior-free approaches. Empirical results further demonstrate that CW-Gen can effectively mitigate the effects of distribution shift.

Problem

• Addressing non-stationarity and distribution shifts in multivariate time series forecasting
• Incorporating conditional means and covariances as informative priors in generative models
• Improving sample quality by replacing standard normal terminal distributions with parameterized ones

Innovation

• Conditional whitening framework incorporates prior information
• Joint Mean-Covariance Estimator learns conditional statistics simultaneously
• Replaces standard normal with parameterized multivariate normal distribution