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.

Towards a robust criterion of anomalous diffusion

“…There exist methods to alleviate this problem, e.g., the mean-maximal excursion statistics 36 . Moreover, Bayesianmaximum-likelihood methods [37][38][39] , deep learning strategies [40][41][42][43][44][45] , or feature-based methods 42,43,46,47 also provide the best estimates for α. However, all these methods have their shortcomings.…”

Ergodic characterization of non-ergodic anomalous diffusion processes

“…The rate of generation of time series is exponentially increasing in all areas of physical and life sciences, and the production of ad-hoc analytical tools is accompanying this growth [175][176][177]. Many of these attempts use Bayesian [67][68][69][70][71] and ML approaches [47,[72][73][74][75][76], and even unsupervised [77][78][79][80][81][82] to detect specific anomalous diffusion processes and the underlying mathematical model, especially deviation from pure Brownian behavior in terms of the anomalous exponent. However, these attempts still lack the accuracy, sensitivity, and specificity necessary, say, for understanding how diffusion properties change over time due to environmental heterogeneity (e.g., patches with different viscosity on a cellular membrane), time-varying properties of the observable (e.g., different activation states of a molecular motor).…”

“…However, all the above factors make this classification a challenging feat. Therefore, recent attempts include Bayesian [67][68][69][70][71] as well as machine learning (ML) approaches [47,[72][73][74][75][76], and even unsupervised approaches [77][78][79][80][81][82]. However, these attempts are based on predominantly atheoretical selection of features which may not necessarily be related to plausible generating mechanisms [83,84].…”

Extracting, quantifying, and comparing dynamical and biomechanical properties of living matter through single particle tracking

“…142,225 More recently, automatic classification approaches based on Bayesian statistics 180,226 and deep-learning algorithms. [227][228][229][230][231] have been introduced to dissect possible transport models with a given set of trajectories. Another means of extending analysis tools is through the combination of physical data analysis with mathematical time series analysis.…”