  Scientists often use observational time series data to study complex natural
processes, but regression analyses often assume simplistic dynamics. Recent
advances in deep learning have yielded startling improvements to the
performance of models of complex processes, but deep learning is generally not
used for scientific analysis. Here we show that deep learning can be used to
analyze complex processes, providing flexible function approximation while
preserving interpretability. Our approach relaxes standard simplifying
assumptions (e.g., linearity, stationarity, and homoscedasticity) that are
implausible for many natural systems and may critically affect the
interpretation of data. We evaluate our model on incremental human language
processing, a domain with complex continuous dynamics. We demonstrate
substantial improvements on behavioral and neuroimaging data, and we show that
our model enables discovery of novel patterns in exploratory analyses, controls
for diverse confounds in confirmatory analyses, and opens up research questions
that are otherwise hard to study.
