Part of the code is from https://github.com/txie-93/cgcnn, and from http://people.kyb.tuebingen.mpg.de/arthur/indep.htm, thank you!
The mathematical problem of statistical independence is examined from a contemporary perspective with a language marked by functional analysis and measure theory. We introduce the necessary conceptual framework in order to achieve this objective and then rigorously develop the two formalisms that historically guided the evolution of the study of independence, as well as the surprising parallelism between them. Crossing the border between the population and empirical worlds, we present in a concise way a corpus of results related to U-statistics, a fundamental abstraction of estimation theory. The purpose of this chapter is to provide the machinery needed to give way to the empirical formulation of testing given a sample whether two random variables are independent or not. Finally, the original contributions are condensed in the two following chapters, providing a bridge between what has been exposed up to this point and the most current machine learning theory, in order to show the applicability of this work in the field of materials physics and the novel representation of their structure in the form of graphs.
Statistical theory, probability, machine learning, materials design, Hilbert spaces, Energy statistics, kernel embeddings, U-statistics, measure theory, solid-state physics, functional analysis, graph theory.