Fast Kalman filtering on quasilinear dendritic trees

Abstract

Event Abstract Back to Event Fast Kalman filtering on quasilinear dendritic trees Liam Paninski1* 1 Columbia University, United States The problem of understanding dendritic computation remains a key open challenge in cellular and computational neuroscience. The major difficulty is in recording physiological signals (especially voltage) with sufficient spatiotemporal resolution on dendritic trees: multiple-electrode recordings from dendrites are quite technically challenging, and provide spatially-incomplete observations, while high-resolution imaging techniques provide more spatially-complete observations, but with significantly lower signal-to-noise. One avenue for extending the reach of these currently available methods is to develop statistical techniques for optimally combining, filtering, and deconvolving these noisy signals. State-space filtering methods are attractive here, since these methods allow us to quite transparently incorporate 1) realistic, spatially-complex multicompartmental models of dendritic dynamics and 2) time-varying, heterogeneous observations (e.g., spatially-scanned multiphoton imaging data) into our filtering equations. The problem is that the time-varying state vector in this problem — which includes, at least, the vector of voltages at every compartment — is very high-dimensional: realistic multicompartmental models often have on the order of N ~10^4 compartments. Standard implementations of state-space filter methods (e.g., the Kalman filter) require O(N^3) time, and are therefore impractical for applications to large dendritic trees. However, we may take advantage of three special features of the dendritic filtering problem to construct efficient filtering methods. First, dendritic dynamics are governed by a cable equation on a tree, which may be solved using symmetric sparse matrix methods in O(N) time. Second, current methods for imaging dendritic voltage provide low SNR observations, as discussed above. Finally, in typical experiments we record only a few image observations (n < 100 or so coarse pixels) at a time. Taken together, these special features allow us to approximate the Kalman equations in terms of a low-rank perturbation of the steady-state (zero-SNR) solution, which in turn may be obtained in O(N) time using efficient matrix solving methods that exploit the sparse tree structure of the dynamics. The resulting methods provide a very good approximation to the exact Kalman solution, but only require O(N) time and space. In addition, a number of extensions of the basic method are possible: for example, we can incorporate spatially blurred or scanned observations; temporally filtered observations and inhomogenous noise sources on the tree; “quasi-active” resonant membrane dynamics; and even in some cases nonlinear observations of the membrane state. Simulation results using the resulting filter allow us to quantify exactly how much information we can expect to extract about dendritic dynamics from recordings at a given SNR. Conference: Computational and Systems Neuroscience 2010, Salt Lake City, UT, United States, 25 Feb - 2 Mar, 2010. Presentation Type: Poster Presentation Topic: Poster session I Citation: Paninski L (2010). Fast Kalman filtering on quasilinear dendritic trees. Front. Neurosci. Conference Abstract: Computational and Systems Neuroscience 2010. doi: 10.3389/conf.fnins.2010.03.00009 Copyright: The abstracts in this collection have not been subject to any Frontiers peer review or checks, and are not endorsed by Frontiers. They are made available through the Frontiers publishing platform as a service to conference organizers and presenters. The copyright in the individual abstracts is owned by the author of each abstract or his/her employer unless otherwise stated. Each abstract, as well as the collection of abstracts, are published under a Creative Commons CC-BY 4.0 (attribution) licence (https://creativecommons.org/licenses/by/4.0/) and may thus be reproduced, translated, adapted and be the subject of derivative works provided the authors and Frontiers are attributed. For Frontiers’ terms and conditions please see https://www.frontiersin.org/legal/terms-and-conditions. Received: 17 Feb 2010; Published Online: 17 Feb 2010. * Correspondence: Liam Paninski, Columbia University, New York, United States, liam@gatsby.ucl.ac.uk Login Required This action requires you to be registered with Frontiers and logged in. To register or login click here. Abstract Info Abstract The Authors in Frontiers Liam Paninski Google Liam Paninski Google Scholar Liam Paninski PubMed Liam Paninski Related Article in Frontiers Google Scholar PubMed Abstract Close Back to top Javascript is disabled. Please enable Javascript in your browser settings in order to see all the content on this page.