Flow Matching with Gaussian Process Priors for Probabilistic Time Series Forecasting (2410.03024v2)

Abstract: Recent advancements in generative modeling, particularly diffusion models, have opened new directions for time series modeling, achieving state-of-the-art performance in forecasting and synthesis. However, the reliance of diffusion-based models on a simple, fixed prior complicates the generative process since the data and prior distributions differ significantly. We introduce TSFlow, a conditional flow matching (CFM) model for time series combining Gaussian processes, optimal transport paths, and data-dependent prior distributions. By incorporating (conditional) Gaussian processes, TSFlow aligns the prior distribution more closely with the temporal structure of the data, enhancing both unconditional and conditional generation. Furthermore, we propose conditional prior sampling to enable probabilistic forecasting with an unconditionally trained model. In our experimental evaluation on eight real-world datasets, we demonstrate the generative capabilities of TSFlow, producing high-quality unconditional samples. Finally, we show that both conditionally and unconditionally trained models achieve competitive results across multiple forecasting benchmarks.

• The paper introduces TSFlow, a novel method that integrates Gaussian Process priors into Conditional Flow Matching for probabilistic time series forecasting.
• The paper demonstrates superior performance with reduced Wasserstein distances and lower Continuous Ranked Probability Scores across multiple datasets.
• The paper shows TSFlow's ability to efficiently generate both conditional and unconditional forecasts, offering practical benefits for real-time applications.

Flow Matching with Gaussian Process Priors for Probabilistic Time Series Forecasting

The paper "Flow Matching with Gaussian Process Priors for Probabilistic Time Series Forecasting" presents TSFlow, a novel approach designed to enhance the generative capabilities of time series models by leveraging Conditional Flow Matching (CFM) with Gaussian Process (GP) priors. This combination seeks to address challenges inherent in traditional diffusion-based models, primarily due to the simplification of optimal transport pathways and integration of data-dependent priors.

Key Contributions

The authors identify several significant contributions through TSFlow:

1. Incorporation of Gaussian Process Priors: The use of Gaussian processes as priors informs the CFM framework, aligning distributions closer to the temporal structure of real-world data. This reduces complexity in the generative process, offering significant improvements over fixed, isotropic Gaussian priors.
2. Conditional and Unconditional Generative Modeling: TSFlow effectively handles both conditional and unconditional scenarios, facilitating high-quality sample generation through informed probability paths. Notably, this involves utilizing both types of models for probabilistic forecasting by strategically incorporating historical data through GP regression.
3. Competitive Performance Evaluation: Extensive comparisons involving eight real-world datasets illustrate TSFlow's competitive edge. The model outperforms existing diffusion-based methods on six datasets, revealing the empirical robustness of the proposed approach.

Experimental Insights

The empirical investigations highlight the significance of optimizing prior distribution choices. TSFlow demonstrates reduced Wasserstein distances from optimal transport maps and enhanced Linear Predictive Scores (LPS) when employing domain-specific GP kernels. Notably, kernels such as Ornstein-Uhlenbeck and periodic kernels provided measurable advantages for specific datasets, confirming that informed priors streamline the generation process.

The paper convincingly shows how TSFlow outperforms conventional methods, achieving lower Continuous Ranked Probability Scores (CRPS) across multiple benchmarks. This suggests TSFlow's capability to produce reliable, statistically consistent forecasts.

Theoretical and Practical Implications

Theoretically, this work enriches the paradigm of flow-based generative models by structuring probability paths with tailored priors. It bridges gaps between unconditional model training and conditional forecasting, applicable across diverse time series contexts, from financial to meteorological data.

Practically, TSFlow's architecture—using DiffWave and S4 layers—demonstrates versatility with manageable computational overhead due to efficient use of Gaussian process regression. This adaptability is particularly relevant in real-time forecasting and applications requiring seamless integration of historical information.

Speculation on Future Directions

Future developments in AI could extend the TSFlow framework to multivariate contexts, exploring the applicability of GP priors in capturing inter-series dependencies. Additionally, leveraging neural forecasting methods with intractable likelihoods might further enhance adaptability and efficiency. Moreover, the exploration of different kernel functions and their impact on varying domains could provide further optimization in probabilistic generative modeling.

In conclusion, the paper introduces TSFlow as a robust alternative in the space of probabilistic time series forecasting, enhancing both theoretical depth and practical effectiveness by integrating Gaussian process-informed paths within conditional flow matching frameworks.