Topological and Mixed-type learning of Brain Activity

Topological characterization of brain imaging data is gaining momentum in the statistical literature, however, the resulting representation of brain imaging data are often defined in complex spaces, not amenable for standard statistical methods. Ad hoc procedures must thus be adopted in order to perform standard statistical tasks such as regression or classification with topological summaries, drastically limiting their use. Exploiting distance-covariance based tests of independence, which can assess the presence of association between object defined in different metric spaces, we build a new class of conditional inference trees, which we call energy trees, that allows to use topological summaries together with more standard covariates, such as categorical variables or graphs, for the analysis of fMRI data.