Training multilayer perceptrons with the extended Kalman algorithm
Advances in neural information processing systems 1
Introduction to the theory of neural computation
Introduction to the theory of neural computation
Spikes: exploring the neural code
Spikes: exploring the neural code
Neural Networks: A Comprehensive Foundation
Neural Networks: A Comprehensive Foundation
Bayesian computation in recurrent neural circuits
Neural Computation
Kalman filter control embedded into the reinforcement learning framework
Neural Computation
A fast learning algorithm for deep belief nets
Neural Computation
Neurocomputing
Neural learning of Kalman filtering, Kalman control, and system identification
IJCNN'09 Proceedings of the 2009 international joint conference on Neural Networks
Winter Simulation Conference
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Although there are many neural network (NN) algorithms for prediction and for control, and although methods for optimal estimation (including filtering and prediction) and for optimal control in linear systems were provided by Kalman in 1960 (with nonlinear extensions since then), there has been, to my knowledge, no NN algorithm that learns either Kalman prediction or Kalman control (apart from the special case of stationary control). Here we show how optimal Kalman prediction and control (KPC), as well as system identification, can be learned and executed by a recurrent neural network composed of linear-response nodes, using as input only a stream of noisy measurement data. The requirements of KPC appear to impose significant constraints on the allowed NN circuitry and signal flows. The NN architecture implied by these constraints bears certain resemblances to the local-circuit architecture of mammalian cerebral cortex. We discuss these resemblances, as well as caveats that limit our current ability to draw inferences for biological function. It has been suggested that the local cortical circuit (LCC) architecture may perform core functions (as yet unknown) that underlie sensory, motor, and other cortical processing. It is reasonable to conjecture that such functions may include prediction, the estimation or inference of missing or noisy sensory data, and the goal-driven generation of control signals. The resemblances found between the KPC NN architecture and that of the LCC are consistent with this conjecture.