Deep kernel learning for geostatistics

Gaussian processes are widely used to make spatial predictions and to estimate uncertainty. But they usually assume that the studied phenomenon has a stationary structure —an assumption often violated with today’s large datasets from sensors or satellites.

To overcome this, this paper explores a space deformation strategy: instead of changing the model, a transformation of the geographic space is learned so that the data is close to stationarity. This transformation is learned with neural networks inspired by normalizing flows, which are well suited for learning complex, reversible mappings.

The transformation is learned by maximizing the model likelihood with gradient-based optimization, using symbolic kernel matrices for scalability. The method is tested on both simulated and real data.

A preprint of the publication can be found here : https://minesparis-psl.hal.science/hal-05165114v2