Abstract

One of the most impressive property of the brain is its ability to continuously extract relevant features from the environment. For example, when surrounded by a noisy crowd, humans can extract the voice of a single person or track its position over time. However, it still remains unknown how this feature extraction takes place in the brain. We formulate this problem in a very general framework where the task is to continuously infer hidden variables given past observations for a an arbitrary nonlinear generative model. Even though, the formal solution to this general problem has been given by the Kushner equation in the form of a stochastic partial differential equation for the posterior distribution, its practical applicability remains difficult due to the closure problem (every moment depends on higher order moments). Here, we propose an approximate yet tractable solution in the form of a sampling based filter. Interestingly, this sampling based filter is biologically plausible and could be implemented by a recurrent network of analog neurons. Furthermore, we derive a learning rule for the parameters of the model. We show through numerical simulations that the performance of this neural filter is as good as a standard particle filter in the limit of large number of particles. Remarkably, when the number of dimensions is large and when the number of particles is limited, the neural filter outperforms the standard particle filter.