An Interpretable and Sparse Neural Network Model for Nonlinear Granger Causality Discovery
This work addresses the need for interpretable causality detection in nonlinear time series, though it appears incremental as it builds on existing neural network methods with specific penalties.
The authors tackled the problem of detecting nonlinear Granger causality in fields like neuroscience and economics by developing a neural network model with group lasso and hierarchical penalties, achieving validation on simulated data from linear and nonlinear models.
While most classical approaches to Granger causality detection repose upon linear time series assumptions, many interactions in neuroscience and economics applications are nonlinear. We develop an approach to nonlinear Granger causality detection using multilayer perceptrons where the input to the network is the past time lags of all series and the output is the future value of a single series. A sufficient condition for Granger non-causality in this setting is that all of the outgoing weights of the input data, the past lags of a series, to the first hidden layer are zero. For estimation, we utilize a group lasso penalty to shrink groups of input weights to zero. We also propose a hierarchical penalty for simultaneous Granger causality and lag estimation. We validate our approach on simulated data from both a sparse linear autoregressive model and the sparse and nonlinear Lorenz-96 model.