- Poster presentation
- Open Access
Approximate nonlinear filtering with a recurrent neural network
BMC Neuroscience volume 16, Article number: P196 (2015)
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.
Starting from the formal mathematical solution to the non-linear filter problem, the Kushner equation , and assuming linear and noisy observations we derive a stochastic rate-based network whose activity samples the posterior dynamics. We found that taking samples following these stochastic posterior dynamics is able to solve the inference task with a performance comparable to that of standard particle filtering or (extended) Kalman filtering. Indeed, for a linear hidden dynamics we exactly retrieve the Kalman filter equations from our neural filter. In Figure 1 we show the error of the filtered estimate as a function of the observation noise for two different parameter choices in our filter equations.
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 .
Kushner H: On the Differential Equations Satisfied by Conditional Probability Densities of Markov Processes, with Applications. Journal of the Society for Industrial & Applied Mathematics. Control. 1962, 2 (1):
Fiser J, Berkes P, Orbán G, Lengyel M: Statistically optimal perception and learning: from behavior to neural representations. Trends in Cognitive Sciences. 2010, 14 (3): 119-130.
Rights and permissions
This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.
About this article
Cite this article
Kutschireiter, A., Surace, S.C., Sprekeler, H. et al. Approximate nonlinear filtering with a recurrent neural network. BMC Neurosci 16 (Suppl 1), P196 (2015). https://doi.org/10.1186/1471-2202-16-S1-P196
- Kalman Filter
- Particle Filter
- Extended Kalman Filter
- Recurrent Neural Network
- Hide Variable