

Preprint 30/2017
Implementing a Bayes Filter in a Neural Circuit: The Case of Unknown Stimulus Dynamics
Sacha Sokoloski
Contact the author: Please use for correspondence this email.
Submission date: 25. Apr. 2017
Pages: 47
published in: Neural computation, 29 (2017) 9, p. 2450-2490
DOI number (of the published article): 10.1162/NECO_a_00991
Bibtex
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Abstract:
In order to interact intelligently with objects in the world, animals
must first transform neural population responses into estimates of the
dynamic, unknown stimuli which caused them. The Bayesian solution
to this problem is known as a Bayes filter, which applies Bayes’ rule to
combine population responses with the predictions of an internal model.
The internal model of the Bayes filter is based on the true stimulus dynamics,
and in this paper we present a method for training a theoretical
neural circuit to approximately implement a Bayes filter when the stimulus
dynamics are unknown. To do this we use the inferential properties
of linear probabilistic population codes to compute Bayes’ rule, and train
a neural network to compute approximate predictions by the method of
maximum likelihood. In particular, we perform stochastic gradient descent
on the negative log-likelihood of the neural network parameters
with a novel approximation of the gradient. We demonstrate our methods
on a finite-state, a linear, and a nonlinear filtering problem, and show
how the hidden layer of the neural network develops tuning curves which
are consistent with findings in experimental neuroscience.