  The brain must extract behaviorally relevant latent variables from the
signals streamed by the sensory organs. Such latent variables are often encoded
in the dynamics that generated the signal rather than in the specific
realization of the waveform. Therefore, one problem faced by the brain is to
segment time series based on underlying dynamics. We present two algorithms for
performing this segmentation task that are biologically plausible, which we
define as acting in a streaming setting and all learning rules being local. One
algorithm is model-based and can be derived from an optimization problem
involving a mixture of autoregressive processes. This algorithm relies on
feedback in the form of a prediction error, and can also be used for
forecasting future samples. In some brain regions, such as the retina, the
feedback connections necessary to use the prediction error for learning are
absent. For this case, we propose a second, model-free algorithm that uses a
running estimate of the autocorrelation structure of the signal to perform the
segmentation. We show that both algorithms do well when tasked with segmenting
signals drawn from autoregressive models with piecewise-constant parameters. In
particular, the segmentation accuracy is similar to that obtained from
oracle-like methods in which the ground-truth parameters of the autoregressive
models are known. We provide implementations of our algorithms at
https://github.com/ttesileanu/bio-time-series.
