Change-point detection in anomalous-diffusion trajectories utilising machine-learning-based uncertainty estimates

Abstract

When recording the movement of individual animals, cells or molecules one will often observe changes in their diffusive behaviour at certain points in time along their trajectory. In order to capture the different diffusive modes assembled in such heterogeneous trajectories it becomes necessary to segment them by determining these change-points. Such a change-point detection can be challenging for conventional statistical methods, especially when the changes are subtle. We here apply Bayesian Deep Learning to obtain point-wise estimates of not only the anomalous diffusion exponent but also the uncertainties in these predictions from a single anomalous diffusion trajectory generated according to four theoretical models of anomalous diffusion. We show that we are able to achieve an accuracy similar to single-mode (without change-points) predictions as well as a well calibrated uncertainty predictions of this accuracy. Additionally, we find that the predicted uncertainties feature interesting behaviour at the change-points leading us to examine the capabilities of these predictions for change-point detection. While the series of predicted uncertainties on their own are not sufficient to improve change-point detection, they do lead to a performance boost when applied in combination with the predicted anomalous diffusion exponents.

15 pages, 7 figures, RevTeX

References in corpus (35)

• What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?
• 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
• Single particle tracking in systems showing anomalous diffusion: the role of weak ergodicity breaking
• Economic Fluctuations and Diffusion
• 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
• Elucidating the Origin of Heterogeneous Anomalous Diffusion in the Cytoplasm of Mammalian Cells
• Machine learning method for single trajectory characterization
• Classification of diffusion modes in single-particle tracking data: Feature-based versus deep-learning approach
• Spectral content of a single non-Brownian trajectory
• Measurement of Anomalous Diffusion Using Recurrent Neural Networks
• Development of anomalous diffusion among crowding proteins
• Bayesian deep learning for error estimation in the analysis of anomalous diffusion
• Codifference as a practical tool to measure interdependence
• Nonergodic Diffusion of Single Atoms in a Periodic Potential
• Classification, inference and segmentation of anomalous diffusion with recurrent neural networks
• Brownian motion and beyond: first-passage, power spectrum, non-Gaussianity, and anomalous diffusion
• Machine-Learning Solutions for the Analysis of Single-Particle Diffusion Trajectories
• Characterization of anomalous diffusion classical statistics powered by deep learning (CONDOR)
• Learning physical properties of anomalous random walks using graph neural networks
• Universal spectral features of different classes of random diffusivity processes
• Boosting the performance of anomalous diffusion classifiers with the proper choice of features
• Crosstalk and transitions between multiple spatial maps in an attractor neural network model of the hippocampus: Collective motion of the activity (II)
• Inferring pointwise diffusion properties of single trajectories with deep learning
• Moses, Noah and Joseph Effects in Coupled Lévy Processes
• Bayesian inference of scaled versus fractional Brownian motion
• Characterization of anomalous diffusion through convolutional transformers
• Codifference can detect ergodicity breaking and non-Gaussianity
• AnDi: The Anomalous Diffusion Challenge
• Non-Gaussian displacements in active transport on a carpet of motile cells
• WaveNet-Based Deep Neural Networks for the Characterization of Anomalous Diffusion (WADNet)
• Semantic Segmentation of Anomalous Diffusion Using Deep Convolutional Networks

Cited by in corpus (3)

• Machine Learning Analysis of Anomalous Diffusion
• Anomalous statistics in the Langevin equation with fluctuating diffusivity: from Brownian yet non-Gaussian diffusion to anomalous diffusion and ergodicity breaking
• Recurrent neural network analysis of single trajectories switching between anomalous diffusion states