Neural Granger Causality (1802.05842v2)

Abstract: While most classical approaches to Granger causality detection assume linear dynamics, many interactions in real-world applications, like neuroscience and genomics, are inherently nonlinear. In these cases, using linear models may lead to inconsistent estimation of Granger causal interactions. We propose a class of nonlinear methods by applying structured multilayer perceptrons (MLPs) or recurrent neural networks (RNNs) combined with sparsity-inducing penalties on the weights. By encouraging specific sets of weights to be zero--in particular, through the use of convex group-lasso penalties--we can extract the Granger causal structure. To further contrast with traditional approaches, our framework naturally enables us to efficiently capture long-range dependencies between series either via our RNNs or through an automatic lag selection in the MLP. We show that our neural Granger causality methods outperform state-of-the-art nonlinear Granger causality methods on the DREAM3 challenge data. This data consists of nonlinear gene expression and regulation time courses with only a limited number of time points. The successes we show in this challenging dataset provide a powerful example of how deep learning can be useful in cases that go beyond prediction on large datasets. We likewise illustrate our methods in detecting nonlinear interactions in a human motion capture dataset.

• The paper presents a deep learning approach that captures nonlinear Granger causality via component-wise neural network models.
• It employs structured sparsity penalties, like group lasso and hierarchical penalties, to ensure interpretability and facilitate automatic lag selection.
• Empirical results on both synthetic and real-world datasets demonstrate the framework’s superiority over traditional linear methods in identifying causal structures.

Neural Granger Causality: A Deep Learning Framework for Time Series Structure Discovery

The paper "Neural Granger Causality" introduces a novel framework for discerning nonlinear Granger causal interactions in multivariate time series data using deep learning techniques. Traditional methods for Granger causality primarily assume linear interactions, often leveraging vector autoregressive (VAR) models with linear dependencies. These classical approaches can be limited when dealing with inherently nonlinear real-world phenomena, such as those found in neuroscience and genomics. This paper aims to overcome such limitations by employing neural networks, specifically multilayer perceptrons (MLPs) and long short-term memory networks (LSTMs), to uncover complex, nonlinear dependencies.

The authors propose component-wise modeling where each time series output is predicted individually through a neural network, thus simplifying the disentanglement of causality from different inputs to outputs. The paper emphasizes the significance of using structured sparsity-inducing penalties, such as group lasso and hierarchical penalties, applied to the neural network weights to ensure that irrelevant connections are appropriately pruned. By doing so, the neural networks are not only employed for their predictive power but are also utilized as interpretable models for structure learning.

Key Contributions and Distinctions

1. Nonlinear Granger Causality: Unlike traditional linear approaches, the proposed method allows for capturing nonlinear interactions, making it suitable for complex datasets.
2. Structured Sparsity Penalties: The use of structured penalties ensures that the models remain interpretable and avoid overfitting, even when working with high-dimensional data. The hierarchical penalty, in particular, provides automatic lag selection, which is crucial for capturing temporal dependencies accurately.
3. Component-wise Approach: By constructing a separate model for each time series output, the framework enables a clearer interpretation of causal relationships, avoiding the complexities introduced by joint modeling of all outputs.
4. Empirical Validation: The methodology is validated on both synthetic datasets, such as the Lorenz-96 and VAR models, and real-world datasets, such as the DREAM3 gene expression data and human motion capture data. In these datasets, the neural networks, particularly the cLSTM, demonstrate superior performance in uncovering the underlying causal structure compared to existing linear and nonlinear methods.

Implications and Future Directions

The implications of this research span both theoretical and practical domains. Theoretically, the work extends traditional notions of Granger causality into the nonlinear regime, fostering possibilities for applying deep learning models to more sophisticated causal inference tasks. Practically, the findings suggest that neural network-based methods can outperform classical techniques in settings where nonlinear interactions are prevalent.

In terms of future developments, further exploration is warranted into more advanced neural network architectures, such as those incorporating attention mechanisms, which could refine the causality detection capabilities. Additionally, the proposed framework's adaptability suggests potential applications in broader domains, ranging from economic data analysis to ecological systems modeling, wherever complex interactions are suspected.

Moreover, the integration of these neural models into broader time series analysis platforms may offer enhanced predictive and interpretative tools, driving advancements in fields requiring high-dimensional data interaction analysis. The ability to uncover interpretable structures in complex systems will undoubtedly prompt further research while posing challenges in ensuring model robustness and interpretability.

In conclusion, "Neural Granger Causality" establishes a significant methodological innovation by harnessing the power of neural networks not just for prediction but also for unveiling underlying causal structures in data. The approach charts a course for future research, promising to expand the boundaries of how time series data is analyzed and understood in various scientific and applied contexts.