Peruzzi M (2026) Partial correlation networks of Gaussian processes.
https://arxiv.org/abs/2604.09953
In multivariate analysis, when you work with Gaussian variables,
you start from the covariance matrix and you take it from there:
correlations, independence, factor models,
precision matrix, conditional independence, partial correlations, graphical structure…
it all works really nicely and we have decades of research to guide us through this.
In multivariate geostatistics, when you work with Gaussian processes,
you start from the covariance function and you take it from there:
correlation function, independence, factor models… precision matrix, conditional independence, partial correlations, graphical structure… it all works really nicely and we have decades of research to guide us through this.
ehm, actually… not so much. At least until today 😉
In this article, I show that there does in fact seem to be a way to build a multivariate Gaussian process where the covariance function gives you all the usual things but also a full partial correlation analysis at the process level. You just need to use some form of “inside-out” model. You can use a spectrally inside-out covariance function, or the OG inside-out. But it kind of works the same way.
And so…
In multivariate geostatistics, when you work with Gaussian processes,
you start from an inside-out covariance function and you take it from there:
correlation function, independence, factor models…
precision matrix, conditional independence, partial correlations, graphical structure…
it all works really nicely and we have decades of research to guide us through this.
