Learning minimal representations of stochastic processes with variational autoencoders
This work addresses the difficulty in modeling stochastic processes for applications in science, though it appears incremental as it builds on existing VAE methods.
The paper tackled the problem of characterizing stochastic processes by introducing an unsupervised machine learning approach to determine the minimal set of parameters needed to describe their dynamics, using a β-VAE architecture on simulated diffusion datasets to extract these parameters and generate new trajectories.
Stochastic processes have found numerous applications in science, as they are broadly used to model a variety of natural phenomena. Due to their intrinsic randomness and uncertainty, they are, however, difficult to characterize. Here, we introduce an unsupervised machine learning approach to determine the minimal set of parameters required to effectively describe the dynamics of a stochastic process. Our method builds upon an extended $β$-variational autoencoder architecture. By means of simulated datasets corresponding to paradigmatic diffusion models, we showcase its effectiveness in extracting the minimal relevant parameters that accurately describe these dynamics. Furthermore, the method enables the generation of new trajectories that faithfully replicate the expected stochastic behavior. Overall, our approach enables the autonomous discovery of unknown parameters describing stochastic processes, hence enhancing our comprehension of complex phenomena across various fields.