Bayesian deep learning for error estimation in the analysis of anomalous diffusion

Abstract

Modern single-particle-tracking techniques produce extensive time-series of diffusive motion in a wide variety of systems, from single-molecule motion in living-cells to movement ecology. The quest is to decipher the physical mechanisms encoded in the data and thus to better understand the probed systems. We here augment recently proposed machine-learning techniques for decoding anomalous-diffusion data to include an uncertainty estimate in addition to the predicted output. To avoid the Black-Box-Problem a Bayesian-Deep-Learning technique named Stochastic-Weight-Averaging-Gaussian is used to train models for both the classification of the diffusion model and the regression of the anomalous diffusion exponent of single-particle-trajectories. Evaluating their performance, we find that these models can achieve a well-calibrated error estimate while maintaining high prediction accuracies. In the analysis of the output uncertainty predictions we relate these to properties of the underlying diffusion models, thus providing insights into the learning process of the machine and the relevance of the output.

20 pages, 11 figures, RevTeX, fixed references

References in corpus (13)

• On Calibration of Modern Neural Networks
• Anomalous transport in the crowded world of biological cells
• Lévy walks
• First-passage times in complex scale-invariant media
• Weak ergodicity breaking of receptor motion in living cells stemming from random diffusivity
• Scaled Brownian motion: a paradoxical process with a time dependent diffusivity for the description of anomalous diffusion
• Spectral content of a single non-Brownian trajectory
• Measurement of Anomalous Diffusion Using Recurrent Neural Networks
• Development of anomalous diffusion among crowding proteins
• Classification of particle trajectories in living cells: machine learning versus statistical testing hypothesis for fractional anomalous diffusion
• Bayesian inference of scaled versus fractional Brownian motion
• Codifference can detect ergodicity breaking and non-Gaussianity
• WaveNet-Based Deep Neural Networks for the Characterization of Anomalous Diffusion (WADNet)

Cited by in corpus (18)

• Machine-Learning Solutions for the Analysis of Single-Particle Diffusion Trajectories
• Inferring pointwise diffusion properties of single trajectories with deep learning
• Quantitative evaluation of methods to analyze motion changes in single-particle experiments
• Modelling intermittent anomalous diffusion with switching fractional Brownian motion
• Non-Gaussian displacements in active transport on a carpet of motile cells
• Semantic Segmentation of Anomalous Diffusion Using Deep Convolutional Networks
• Heterogeneous biological membranes regulate protein partitioning via fluctuating diffusivity
• Diffusion of intrinsically disordered proteins within viscoelastic membraneless droplets
• Multifractional Brownian motion with telegraphic, stochastically varying exponent
• Anomalous diffusion, non-Gaussianity, and nonergodicity for subordinated fractional Brownian motion with a drift
• Machine Learning Analysis of Anomalous Diffusion
• Preface: Characterisation of Physical Processes from Anomalous Diffusion Data
• Change-point detection in anomalous-diffusion trajectories utilising machine-learning-based uncertainty estimates
• Anomalous statistics in the Langevin equation with fluctuating diffusivity: from Brownian yet non-Gaussian diffusion to anomalous diffusion and ergodicity breaking
• Inferring the Langevin Equation with Uncertainty via Bayesian Neural Networks
• Recurrent neural network analysis of single trajectories switching between anomalous diffusion states
• Loss-Complexity Landscape and Model Structure Functions
• Improved mean squared displacement analysis for anomalous single particle trajectories