Here the concept of Granger causality is employed to propose a new criterion for unsupervised learning that is appropriate in the case of temporally-dependent source signals. The basic idea is to identify two projections of a multivariate time series such that the Granger causality among the resulting pair of components is maximized.

We consider the problem of variational Bayesian inference in a latent variable model where a (possibly complex) observed stochastic process is governed by the solution of a latent stochastic differential equation (SDE).

We present a multi-temporal, multi-modal remote-sensing dataset for predicting how active wildfires will spread at a resolution of 24 hours. The dataset consists of 13 607 images across 607 fire events in the United States from January 2018 to October 2021. For each fire event, the dataset contains a full time series of daily observations, containing detected active fires and variables related to fuel, topography and weather conditions. The dataset is challenging due to: a) its inputs being multi-temporal, b) the high number of 23 multi-modal input channels, c) highly imbalanced labels and d) noisy labels, due to smoke, clouds, and inaccuracies in the active fire detection.

However, existing contrastive learning methods primarily focus on one single data level, which fails to fully exploit the intricate nature of medical time series.

Specifically, we lay the foundation within the Bayesian framework.