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Learning non-stationary Langevin dynamics from stochastic observations of latent trajectories

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Listed:
  • Mikhail Genkin

    (Cold Spring Harbor Laboratory)

  • Owen Hughes

    (University of Michigan)

  • Tatiana A. Engel

    (Cold Spring Harbor Laboratory)

Abstract

Many complex systems operating far from the equilibrium exhibit stochastic dynamics that can be described by a Langevin equation. Inferring Langevin equations from data can reveal how transient dynamics of such systems give rise to their function. However, dynamics are often inaccessible directly and can be only gleaned through a stochastic observation process, which makes the inference challenging. Here we present a non-parametric framework for inferring the Langevin equation, which explicitly models the stochastic observation process and non-stationary latent dynamics. The framework accounts for the non-equilibrium initial and final states of the observed system and for the possibility that the system’s dynamics define the duration of observations. Omitting any of these non-stationary components results in incorrect inference, in which erroneous features arise in the dynamics due to non-stationary data distribution. We illustrate the framework using models of neural dynamics underlying decision making in the brain.

Suggested Citation

  • Mikhail Genkin & Owen Hughes & Tatiana A. Engel, 2021. "Learning non-stationary Langevin dynamics from stochastic observations of latent trajectories," Nature Communications, Nature, vol. 12(1), pages 1-9, December.
  • Handle: RePEc:nat:natcom:v:12:y:2021:i:1:d:10.1038_s41467-021-26202-1
    DOI: 10.1038/s41467-021-26202-1
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    References listed on IDEAS

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    1. Postnikov, Eugene B. & Sokolov, Igor M., 2019. "Reconstruction of substrate’s diffusion landscape by the wavelet analysis of single particle diffusion tracks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 533(C).
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    3. Josef Ladenbauer & Sam McKenzie & Daniel Fine English & Olivier Hagens & Srdjan Ostojic, 2019. "Inferring and validating mechanistic models of neural microcircuits based on spike-train data," Nature Communications, Nature, vol. 10(1), pages 1-17, December.
    4. Bryan C. Daniels & Ilya Nemenman, 2015. "Automated adaptive inference of phenomenological dynamical models," Nature Communications, Nature, vol. 6(1), pages 1-8, November.
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