A neural network implementing optimal state estimation
based on dynamic spike train decoding
Omer Bobrowski, Ron Meir, Shy Shoham and Yonina Eldar
In: NIPS 2007, December 2007, Vancouver, Canada.
It is becoming increasingly evident that organisms acting in
uncertain dynamical environments often employ exact or approximate
Bayesian statistical calculations in order to continuously
estimate the environmental state, integrate information from
multiple sensory modalities, form predictions and choose actions.
What is less clear is how these putative computations are
implemented by cortical neural networks. An additional level of
complexity is introduced because these networks observe the world
through spike trains received from primary sensory afferents,
rather than directly. A recent line of research has described
mechanisms by which such computations can be implemented using a
network of neurons whose activity directly represents a
probability distribution across the possible ``world states''.
Much of this work, however, uses various approximations, which
severely restrict the domain of applicability of these
implementations. Here we make use of rigorous mathematical results
from the theory of continuous time point process filtering, and
show how optimal real-time state estimation and prediction may be
implemented in a general setting using linear neural networks. We
demonstrate the applicability of the approach with several
examples, and relate the required network properties to the
statistical nature of the environment, thereby quantifying the
compatibility of a given network with its environment.