This paper tackles a new regression problem, called Dynamic Time-Lag Regression (DTLR), where a cause signal drives an effect signal with an unknown time delay. The motivating application, pertaining to space weather modelling, aims to predict the near-Earth solar wind speed based on estimates of the Sun’s coronal magnetic field. DTLR differs from mainstream regression and from sequence-to-sequence learning in two respects: firstly, no ground truth (e.g., pairs of associated sub-sequences) is available; secondly, the cause signal contains much information irrelevant to the effect signal (the solar magnetic field governs the solar wind propagation in the heliosphere, of which the Earth’s magnetosphere is but a minuscule region).A Bayesian approach is presented to tackle the specifics of the DTLR problem,with theoretical justifications based on linear stability analysis. A proof of concept on synthetic problems is presented. Finally, the empirical results on the solar wind modelling task improve on the state of the art in solar wind forecasting.

International Conference on Learning Representations (ICLR)
Multiscale Dynamics

Chandorkar, M., Camporeale, E., Furtlehner, C., Poduval, B., & Sebag, M. (2020). Dynamic time-lag regression: Predicting what & when. In Eighth International Conference on Learning Representations.