Abstract

Please join us for our fortnightly journal club online via zoom where two presenters will jointly present a topic together. The next topic is ‘Nonlinear filtering in neuroscience’ presented by Jean-Pascal Pfister and Xizi Li.

Zoom information: https://us02web.zoom.us/j/84958321096?pwd=dFpsYnpJYWVNeHlJbEFKbW1OTzFiQT09

Continuously extracting relevant information from a stream of inputs is a key machine learning problem with a wide range of applications in neuroscience. Formally, this problem – also known as nonlinear (Bayesian) filtering – aims at estimating the posterior distribution (or filtering distribution) at time t of some latent variable given all the inputs up to time t.

This nonlinear filtering theory can be applied in neuroscience from two different perspectives. Firstly, nonlinear filtering can be seen as a data analysis method where the task is to extract relevant information from continuous neural recording (such as continuously estimating the position of a rat based on place cells activity or continuously estimating the intention of a patient in order to control a neuroprothesis). Secondly, nonlinear filtering can be seen as a computational principle that can be applied at different levels such as the behavioural level (e.g. continuously tracking the position of a prey), neuronal level (estimating the causes of the inputs to a neural network) or even single synapse level (e.g estimating the presynaptic membrane potential).

In the first part of this journal club, we will review the theory of nonlinear filtering with the formal solution given by the Kushner-Stratonovic equation. For a tutorial see [1]. We will highlight the limitation of this formal solution in terms of practical applicability and describe the possible approximate solutions. In the second part of the journal club we will discuss one specific application of nonlinear filtering in the context of learning [2,3] and highlight the specific predictions of a synaptic learning rule derived from this nonlinear filtering approach.

Refs:

[1] Kutschireiter, A., Surace, S. C., & Pfister, J.-P. (2020). The Hitchhiker’s guide to nonlinear filtering. Journal of Mathematical Psychology, 94, 102307. http://doi.org/10.1016/j.jmp.2019.102307

[2] Aitchison, L., Jegminat, J., Menendez, J. A., Pfister, J.-P., Pouget, A., & Latham, P. E. (2021). Synaptic plasticity as Bayesian inference. Nature Neuroscience, 24, 565–571. http://doi.org/10.1038/s41593-021-00809-5

[3] Jegminat, J., & Pfister, J.-P. (2020). Learning as filtering: implications for spike-based plasticity. arXiv:2008.03198