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

TL;DR

This paper introduces a machine learning approach using Bayesian Deep Learning to detect change-points in anomalous diffusion trajectories by estimating diffusion parameters and their uncertainties, improving detection when combined with diffusion exponents.

Contribution

It presents a novel application of Bayesian Deep Learning for simultaneous estimation of diffusion parameters and uncertainties, enhancing change-point detection in complex trajectories.

Findings

Achieves comparable accuracy to single-mode predictions

Uncertainties are well calibrated and informative at change-points

Combining uncertainties with diffusion exponents improves change-point detection

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.