Scalable Bayesian inference of dendritic voltage via spatiotemporal - - PowerPoint PPT Presentation

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Scalable Bayesian inference of dendritic voltage via spatiotemporal - - PowerPoint PPT Presentation

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Scalable Bayesian inference of dendritic voltage via spatiotemporal recurrent state space models Ruoxi Sun*, Scott Linderman*, Ian Kinsella, Liam Paninski Columbia University NeurIPS 2019 Dendritic voltage imaging Hochbaum et al Nature Methods,

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Scalable Bayesian inference of dendritic voltage via spatiotemporal recurrent state space models

Ruoxi Sun*, Scott Linderman*, Ian Kinsella, Liam Paninski Columbia University NeurIPS 2019

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Dendritic voltage imaging

Hochbaum et al Nature Methods, 2014

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https://biology.stackexchange.com/questions/44082/can-the-dendrites-of-sensory-neurons-be-a-meter-long

Multiple Compartment models

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https://biology.stackexchange.com/questions/44082/can-the-dendrites-of-sensory-neurons-be-a-meter-long

Multiple Compartment models

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https://biology.stackexchange.com/questions/44082/can-the-dendrites-of-sensory-neurons-be-a-meter-long

Multiple Compartment models

Compartment 1 2 3 4

1 4 3 2

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Biophysics

Compartment n: Cable equation theory

g: conductance; I: current; R: resistance; V: voltage; C: capacitance

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Biophysics to Statistics Model

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Model Single Compartment Dynamics one time step

theta: parameters Z: discrete latent variable X: continuous latent variable (cycle parameters) V: continuous latent variable (denoised voltage) Y: observed variables

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Model Single Compartment Dynamics

  • Recurrent Switching Linear Dynamical System (rSLDs)
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Statistical Model

Physical model

theta: parameters; Z: discrete latent variable; X: continuous latent variable (cycle parameters); V: continuous latent variable (denoised voltage); Y: observed variables

  • Recurrent Switching Linear Dynamical System (rSLDs)
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  • Recurrent Switching Linear Dynamical System (rSLDs)

Statistical Model

Linderman et al (AISTATS 2017)

theta: parameters; Z: discrete latent variable; X: continuous latent variable (cycle parameters); V: continuous latent variable (denoised voltage); Y: observed variables

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Model Inter-Compartment Dynamics

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Linear Dependency between Adjacent Compartments

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Results: Single Compartment

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Output of the model for Single Compartment model

  • Observed Voltage (y)
  • Inferred Continuous Latent State: V (voltage) and X (cycle)

V

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  • Inferred Discrete Latent State (Z)
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  • Generated new spike (voltage)
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Results: Multiple Compartments

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Multiple Compartment denoising

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Inferred Voltage

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Thank you! Poster: #147 Code: https://github.com/SunRuoxi/Voltage_Smoothing_with_rSLDS

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Previous Biophysical work

  • Hodgkin Huxley
  • Fitzhugh-Nagumo