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© Research
Publication : Physical review. E

Variational inference of fractional Brownian motion with linear computational complexity.

Scientific Fields
Diseases
Organisms
Applications
Technique

Published in Physical review. E - 01 Nov 2022

Verdier H, Laurent F, Cassé A, Vestergaard CL, Masson JB,

Link to Pubmed [PMID] – 36559393

Link to DOI – 10.1103/PhysRevE.106.055311

Phys Rev E 2022 Nov; 106(5-2): 055311

We introduce a simulation-based, amortized Bayesian inference scheme to infer the parameters of random walks. Our approach learns the posterior distribution of the walks’ parameters with a likelihood-free method. In the first step a graph neural network is trained on simulated data to learn optimized low-dimensional summary statistics of the random walk. In the second step an invertible neural network generates the posterior distribution of the parameters from the learned summary statistics using variational inference. We apply our method to infer the parameters of the fractional Brownian motion model from single trajectories. The computational complexity of the amortized inference procedure scales linearly with trajectory length, and its precision scales similarly to the Cramér-Rao bound over a wide range of lengths. The approach is robust to positional noise, and generalizes to trajectories longer than those seen during training. Finally, we adapt this scheme to show that a finite decorrelation time in the environment can furthermore be inferred from individual trajectories.

https://pubmed.ncbi.nlm.nih.gov/36559393