Connecting the Dots: Multivariate Time Series Forecasting with Graph Neural Networks (2005.11650v1)

Abstract: Modeling multivariate time series has long been a subject that has attracted researchers from a diverse range of fields including economics, finance, and traffic. A basic assumption behind multivariate time series forecasting is that its variables depend on one another but, upon looking closely, it is fair to say that existing methods fail to fully exploit latent spatial dependencies between pairs of variables. In recent years, meanwhile, graph neural networks (GNNs) have shown high capability in handling relational dependencies. GNNs require well-defined graph structures for information propagation which means they cannot be applied directly for multivariate time series where the dependencies are not known in advance. In this paper, we propose a general graph neural network framework designed specifically for multivariate time series data. Our approach automatically extracts the uni-directed relations among variables through a graph learning module, into which external knowledge like variable attributes can be easily integrated. A novel mix-hop propagation layer and a dilated inception layer are further proposed to capture the spatial and temporal dependencies within the time series. The graph learning, graph convolution, and temporal convolution modules are jointly learned in an end-to-end framework. Experimental results show that our proposed model outperforms the state-of-the-art baseline methods on 3 of 4 benchmark datasets and achieves on-par performance with other approaches on two traffic datasets which provide extra structural information.

Connecting the Dots: Multivariate Time Series Forecasting with Graph Neural Networks

The paper "Connecting the Dots: Multivariate Time Series Forecasting with Graph Neural Networks" presents a novel approach to modeling and forecasting multivariate time series (MTS) data through Graph Neural Networks (GNNs). This method leverages the inherent spatial and temporal dependencies within the data, employing a specifically designed GNN framework that includes several innovative components such as a graph learning layer, a mix-hop propagation layer, and a dilated inception layer.

Key Contributions

1. Graph Learning Layer: The paper introduces a graph learning module that constructs an adjacency matrix to capture latent spatial dependencies among the variables in the MTS. Unlike traditional GNNs that require a pre-defined graph structure, this module learns the graph structure from the data, making the approach more flexible. The learning layer employs node embeddings to determine the pairwise relationships and ensures that the resultant graph is uni-directional, which aligns well with the causal nature often present in time series data.
2. Mix-hop Propagation Layer: This layer addresses the over-smoothing issue commonly encountered in GNNs by incorporating both node-self and neighborhood information in a controlled manner. By retaining a portion of the original node states during information propagation, the layer preserves the local features while capturing higher-order dependencies across the graph.
3. Dilated Inception Layer: To efficiently capture temporal dependencies with varying frequencies, the dilated inception layer combines multiple kernel sizes and dilation factors. This hybrid approach ensures the model can handle both short-term and long-term dependencies within the time series data.
4. End-to-End Framework: The model integrates the graph learning, graph convolution, and temporal convolution modules into a cohesive end-to-end framework. The parameters are jointly optimized, which bridges the learning of spatial and temporal dependencies, enhancing the forecasting accuracy.

Experimental Validation

The effectiveness of the proposed model, termed MTGNN, is demonstrated through extensive evaluations on various benchmark datasets including traffic, solar-energy, electricity, and exchange-rate. The results show that MTGNN frequently outperforms state-of-the-art methods in both single-step and multi-step forecasting tasks. Particularly notable improvements are observed in the traffic dataset, which validates the model's capability in handling complex spatial dependencies common in such data.

The MTGNN model performs exceptionally well even when compared with other spatial-temporal graph neural networks like DCRNN, STGCN, and Graph WaveNet, despite not requiring pre-defined graph structures. This highlights the robustness and adaptability of the graph learning layer in constructing meaningful adjacency matrices from data.

Implications

Practical Implications

1. Versatility: By eliminating the need for predefined graph structures, MTGNN is applicable to a wider array of MTS datasets where such structures are not available or are difficult to define.
2. Scalability: The proposed graph sampling strategy reduces computation and memory overhead, making the method scalable for large datasets and extensive time sequences.

Theoretical Implications

1. Graph Learning in Neural Networks: The success of the graph learning layer propels forward the notion of integrating graph structure discovery within the training process of neural networks. This opens avenues for more advanced methods that dynamically adjust graph structures based on evolving data correlations.
2. Propagation Control: The mix-hop propagation layer's approach to handling over-smoothing in GNNs possibly invites more research into propagation control mechanisms within graph convolution operations.

Future Prospects

The paper sets a solid foundation for future research along several lines:

1. Dynamic Adjustments: Extending the model to dynamically adjust the learned graph structure in response to real-time data streams, thereby enhancing adaptability in non-stationary environments.
2. Hybrid Models: Integrating MTGNN with other learning paradigms such as reinforcement learning or unsupervised pre-training to enhance its capability and application scope.
3. Extended Applications: Applying the MTGNN framework to a broader spectrum of domains, such as healthcare, climate modeling, and financial forecasting, to validate its generalization capabilities and fine-tune domain-specific adaptations.

In summary, this paper presents a comprehensive and effective approach to MTS forecasting using GNNs. The proposed MTGNN framework's strong performance across various datasets underscores its potential as a versatile tool for capturing complex dependencies in time series data, paving the way for future advancements in this area of research.