ESI

Ensemble Spatial Interpolation - ESI

Ensemble Spatial Interpolation (ESI) is a core investigation at ALGES, compromising various of the laboratory’s research areas.

This line of research has generated a revolutionary method for spatial interpolation that has been shown to be equivalent to Kriging under linearity assumptions, but without the need for a variogram. Furthermore, ESI is a non-linear method capable of making estimations in highly non-stationary domains.

ESI employs ensemble learning, where multiple predictions or ‘weak votes’ are integrated into a strong ensemble response. Correspondingly, ESI aggregates a set of weak interpolation functions, each based on different spatial configurations. This approach has demonstrated to yield robust estimates, while efficiently handling large datasets and providing uncertainty quantifications (Egaña et al., 2021).

Methodology

Inspired by the concept of bootstrapping the space (Egaña et al., 2021), ESI begins by generating a set of distinct random partitions of the study area using ‘Mondrian Tree’ stochastic procesess. Each partition cell contains a unique data subset, suitable for any interpolation method.

To assess unmeasured locations, ESI performs interpolations within each encompassing cell -one per partition- employing the relevant subset of data points. The process concludes with the aggregation of all values.

Both global ordinary kriging and inverse distance weighting (IDW) have been explored as the base interpolator for ESI. The latter has become a focal point of research for its straightforward implementation and its efficacy in overcoming the smoothing effect and inductive biases associated with kriging. Other alternatives are currently being studied.

Implementation

Along with this research, a software library that implements the method has been developed and is soon to be released to the scientific community. This user-friendly tool -called Spatialize- aims to make advanced geostatistics accesible to a broader audience.