Generative Time Series Forecasting with Diffusion, Denoise, and Disentanglement (2301.03028v1)

Abstract: Time series forecasting has been a widely explored task of great importance in many applications. However, it is common that real-world time series data are recorded in a short time period, which results in a big gap between the deep model and the limited and noisy time series. In this work, we propose to address the time series forecasting problem with generative modeling and propose a bidirectional variational auto-encoder (BVAE) equipped with diffusion, denoise, and disentanglement, namely D3VAE. Specifically, a coupled diffusion probabilistic model is proposed to augment the time series data without increasing the aleatoric uncertainty and implement a more tractable inference process with BVAE. To ensure the generated series move toward the true target, we further propose to adapt and integrate the multiscale denoising score matching into the diffusion process for time series forecasting. In addition, to enhance the interpretability and stability of the prediction, we treat the latent variable in a multivariate manner and disentangle them on top of minimizing total correlation. Extensive experiments on synthetic and real-world data show that D3VAE outperforms competitive algorithms with remarkable margins. Our implementation is available at https://github.com/PaddlePaddle/PaddleSpatial/tree/main/research/D3VAE.

• The paper proposes a coupled diffusion probabilistic model integrated with a BVAE to mitigate aleatoric uncertainty and enhance data representation.
• It incorporates multiscale denoising score matching to guide the generative process, yielding cleaner predictions and superior accuracy over baselines.
• Through disentangled latent variables and extensive experiments, the model achieves marked improvements in MSE and CRPS on both synthetic and real-world datasets.

Generative Time Series Forecasting with Diffusion, Denoise, and Disentanglement

The paper "Generative Time Series Forecasting with Diffusion, Denoise, and Disentanglement" introduces a novel approach for time series forecasting by employing a Bidirectional Variational Auto-Encoder (BVAE) framework augmented with diffusion, denoising, and disentanglement techniques, namely D$^3$.

Key Contributions

1. Coupled Diffusion Probabilistic Model:
   • The authors present a coupled diffusion probabilistic model to augment both input and target time series data. This approach aims to mitigate the intrinsic aleatoric uncertainty typical in real-world time series data without adding extra randomness.
   • By applying a forward diffusion process that gradually adds Gaussian noise, the model enhances the tractability and expressiveness of the generative model.
   • A backward process modeled by the BVAE facilitates the inference, leveraging the deep hierarchical structure of VAEs to capture the latent distributions efficiently.
2. Multiscale Denoising:
   • To ensure generated time series approximate the true target, the authors incorporate multiscale denoising score matching into the diffusion process. This mechanism operates by constructing a score network that provides gradients of the log-density concerning the noisy data, effectively guiding the generative model towards cleaner predictions.
   • This denoising step addresses potential deficits arising from the diffusion process, where added noise might corrupt the samples.
3. Latent Variable Disentanglement:
   • The paper highlights the importance of interpretability in time series forecasting. By treating the latent variables in a multivariate manner and disentangling them based on minimizing total correlation (TC), the model enhances interpretability and prediction stability.
   • Disentangled representations correspond to independent factors influencing the temporal patterns, facilitating a more reliable and interpretable model.

Experimental Validation

The effectiveness of the D$^3$ model is substantiated through extensive experiments on both synthetic and real-world datasets. The results reveal significant improvements over competitive baselines such as NVAE, $\beta$-TCVAE, DeepAR, and TimeGrad in terms of Mean Squared Error (MSE) and Continuous Ranked Probability Score (CRPS).

Key numerical findings include:

• Synthetic Data: On synthetic datasets D$_1$ and D$_2$, D$^3$ consistently outperforms other models, achieving lower MSE and CRPS values, thereby demonstrating its robust generalization capabilities.
• Real-World Data: Testing on multiple real-world datasets (Traffic, Electricity, Weather, Wind, ETTm1, and ETTh1), D$^3$ provides significant reductions in MSE and CRPS. Notably, for Traffic and Electricity datasets, the reductions are up to 90% and 71% respectively concerning MSE, and 73% and 31% for CRPS.

Implications and Future Directions

1. Robust Time Series Forecasting:
   • The integration of diffusion processes enables augmented datasets without compromising data integrity, thus preventing overfitting and improving generalization—critical for scenarios with limited data.
2. Uncertainty Estimation and Interpretability:
   • The multiscale denoising mechanism and disentangled latent variables contribute to the model's interpretability and reliability. Such interpretable latent space allows for better understanding the underlying temporal dynamics and uncertainty estimation in predictions.
   • Future research can explore more sophisticated disentanglement techniques and extend the usage of score-based generative models in other time series domains.
3. Generative Modeling Techniques:
   • While this work specifically addresses time series, the underlying principles of coupled diffusion and denoising are broadly applicable to other domains. Future advancements might focus on adaptive variance schedules and hybrid generative methods combining EBMs and VAEs.

Overall, the methodologies proposed in this paper contribute substantially to the field of generative time series forecasting, providing a balanced and nuanced approach to tackling the inherent challenges of time series data through advanced generative models and interpretable machine learning techniques.