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A neural implementation for nonlinear filtering


Kutschireiter, A; Surace, S C; Sprekeler, H; Pfister, J P (2015). A neural implementation for nonlinear filtering. Neurons and Cognition q-bio.NC, Institute of Neuroinformatics.

Abstract

The computational task of continuous-time state estimation, nonlinear filtering and identification, i.e.~parameter learning, poses a class of interesting problems, which mathematicians have been working on for over 50 years and which has received increasing attention in both machine-learning and neuroscience communities. Moreover, the question how Bayesian inference in general and nonlinear filtering in particular can be implemented in neuronal tissue might be a step towards understanding information processing in the brain. Yet possible answers to this question remain debated. Starting from the mathematical formalism of nonlinear filtering theory, we propose a stochastic rate-based network in terms of a stochastic differential equation whose activity samples the posterior dynamics. The underlying mathematical framework is flexible enough to additionally allow extensions to other tasks such as parameter learning. We show that the numerical performance of the model is adequate to account for both nonlinear filtering and identification problems. Our network may be implemented as a recurrent neuronal network in a biologically plausible manner and thus offers a concrete proposition of how neural sampling might be implemented in the brain.

Abstract

The computational task of continuous-time state estimation, nonlinear filtering and identification, i.e.~parameter learning, poses a class of interesting problems, which mathematicians have been working on for over 50 years and which has received increasing attention in both machine-learning and neuroscience communities. Moreover, the question how Bayesian inference in general and nonlinear filtering in particular can be implemented in neuronal tissue might be a step towards understanding information processing in the brain. Yet possible answers to this question remain debated. Starting from the mathematical formalism of nonlinear filtering theory, we propose a stochastic rate-based network in terms of a stochastic differential equation whose activity samples the posterior dynamics. The underlying mathematical framework is flexible enough to additionally allow extensions to other tasks such as parameter learning. We show that the numerical performance of the model is adequate to account for both nonlinear filtering and identification problems. Our network may be implemented as a recurrent neuronal network in a biologically plausible manner and thus offers a concrete proposition of how neural sampling might be implemented in the brain.

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Additional indexing

Item Type:Working Paper
Communities & Collections:07 Faculty of Science > Institute of Neuroinformatics
Dewey Decimal Classification:570 Life sciences; biology
Language:English
Date:2015
Deposited On:22 Feb 2016 10:05
Last Modified:08 Dec 2017 18:28
Series Name:Neurons and Cognition
Free access at:Official URL. An embargo period may apply.
Official URL:http://arxiv.org/abs/1508.06818
Other Identification Number:1508.06818

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