Implementing a Bayes Filter in a Neural Circuit: The Case of Unknown Stimulus Dynamics
This work addresses the challenge of how animals can estimate dynamic stimuli from neural responses, with incremental contributions to computational neuroscience and machine learning.
The paper tackled the problem of learning to approximate a Bayes filter for unknown stimulus dynamics by using probabilistic population codes and training a neural network with a novel gradient approximation, demonstrating it on finite-state, linear, and nonlinear filtering problems and showing that the network's hidden layer develops tuning curves consistent with experimental neuroscience findings.
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. In this paper we present a method for learning to approximate a Bayes filter when the stimulus dynamics are unknown. To do this we use the inferential properties of 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 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.