mlsanityData to 14 Oct 2026

Variational inference of fractional Brownian motion with linear computational complexity

arXiv 2203.07961 ↗First posted 15 Mar 2022cs.LG physics.bio-ph physics.data-ancited by 4

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Abstract (arXiv)

We introduce a simulation-based, amortised 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 learnt 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 Cram'er-Rao bound over a wide range of lengths. The approach is robust to positional noise, and generalizes well 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.

Key facts. Cited by 4 papers in the map (data through 14 Oct 2026). Builds on 23 of its 82 references that are in the map. First posted on arXiv 15 Mar 2022.

Builds on

23 of 82 references.

References · 23

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11 more
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Cited by year

Citing papers per year: 2023: 2; 2024: 1; 2025: 1.

4 papers.

  1. 2023BayesFlow: Amortized Bayesian Workflows With Neural Networkscited by 32
  2. 2024Machine Learning Analysis of Anomalous Diffusioncited by 3
  3. 2023Machine-Learning Solutions for the Analysis of Single-Particle Diffusion Trajectoriescited by 2
  4. 2025Data-Efficient Learning of Anomalous Diffusion with Wavelet Representations: Enabling Direct Learning from Experimental Trajectoriescited by 0