Variational inference of fractional Brownian motion with linear computational complexity

Hippolyte Verdier, François Laurent, Alhassan Cassé, Christian L. Vestergaard, and Jean-Baptiste Masson
Phys. Rev. E 106, 055311 – Published 22 November 2022

Abstract

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.

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  • Received 17 March 2022
  • Accepted 11 October 2022

DOI:https://doi.org/10.1103/PhysRevE.106.055311

©2022 American Physical Society

Physics Subject Headings (PhySH)

Physics of Living Systems

Authors & Affiliations

Hippolyte Verdier1,2,*, François Laurent1, Alhassan Cassé2, Christian L. Vestergaard1, and Jean-Baptiste Masson1,†

  • 1Decision and Bayesian Computation, USR 3756 (C3BI/DBC) and Neuroscience Department CNRS UMR 3751, Institut Pasteur, Université de Paris, CNRS, 75015 Paris, France
  • 2Histopathology and Bio-Imaging Group, Sanofi, R&D, 94400 Vitry-Sur-Seine, France

  • *hverdier@pasteur.fr
  • jbmasson@pasteur.fr

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Issue

Vol. 106, Iss. 5 — November 2022

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