  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.
