Optimal nonlinear filtering with neural networks
A remarkable property of the brain is its ability to continuously extract relevant features in a changing environment. This task becomes even more challenging when we realize that sensory inputs are not perfectly reliable. 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. However, it remains unclear how these filtering algorithms may be implemented in neural tissue. The aim of this project is to propose a neuronal dynamics which approximates this non-linear filtering.