System identification in the brain: inferring ARMA dynamics from sensory data

Sensory information reaches the brain as a stream with non-trivial correlations across time. In a generative model, these correlations can be seen as the result of a dynamical system acting on a white noise source signal. Learning the parameters describing this system enables a variety of applications, from detecting changes in the input dynamics to inferring dynamical rules in the environment.

Here we present biologically plausible neural networks for performing system identification from time series data. The starting point is the mutual information between the past and the future, which in the case of one-dimensional Gaussian signals is equal to a kind of cepstral norm. By searching for the autoregressive moving-average (ARMA) filter that minimizes this mutual information, we develop algorithms that learn an inverse model to the dynamical system generating the data. Employing update rules based on Givens rotations we ensure that our algorithms work online, an essential ingredient to maintain biological plausibility. We also look for implementations that rely on local learning rules, such that synaptic updates only require information that is available to them from pre- and post- synaptic activity.