Approximate nonlinear filtering with a recurrent neural network
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KeywordsKalman Filter Particle Filter Extended Kalman Filter Recurrent Neural Network Hide Variable
One of the most fascinating properties of the brain is its ability to continuously extract relevant features in a changing environment. Realizing that sensory inputs are not perfectly reliable, this task becomes even more challenging. This problem can be formalized as a filtering problem where the aim is to infer the state of a dynamically changing hidden variable given some noisy observation. A well-known solution to this problem is the Kalman filter for linear hidden dynamics or the extended Kalman filter for nonlinear dynamics. On the other hand, particle filters offer a sampling-based approach to approximate the posterior distribution. However, it remains unclear how these filtering algorithms may be implemented in neural tissue. Here, we propose a neuronal dynamics which approximates non-linear filtering.
Thus, the neuronal filter we propose provides an efficient way to infer the state of temporally changing hidden variables. In addition, due to the locality of the underlying mathematical model, the filter is made biologically plausible from a neural-sampling perspective, hence providing a possible framework for the neural sampling hypothesis .
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