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

被引:11
|
作者
Genkin, Mikhail [1 ]
Hughes, Owen [2 ]
Engel, Tatiana A. [1 ]
机构
[1] Cold Spring Harbor Lab, POB 100, Cold Spring Harbor, NY 11724 USA
[2] Univ Michigan, Ann Arbor, MI 48109 USA
关键词
SIGNATURE;
D O I
10.1038/s41467-021-26202-1
中图分类号
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号
07 ; 0710 ; 09 ;
摘要
Langevin dynamics describe transient behavior of many complex systems, however, inferring Langevin equations from noisy data is challenging. The authors present an inference framework for non-stationary latent Langevin dynamics and test it on models of spiking neural activity during decision making. 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.
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页数:9
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