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

TL;DR

This paper enhances machine learning methods for analyzing anomalous diffusion by incorporating Bayesian techniques to provide reliable uncertainty estimates alongside predictions, aiding in understanding physical mechanisms in diverse systems.

Contribution

It introduces a Bayesian deep learning approach using Stochastic-Weight-Averaging-Gaussian for error estimation in diffusion model classification and regression tasks.

Findings

Models achieve well-calibrated error estimates.

High prediction accuracy maintained with uncertainty quantification.

Output uncertainty relates to underlying diffusion properties.

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.