Random forests on distance matrices for imaging genetics studies

Maximal Accurate Forests from Distance Matrices

We present a fast converging method for distance-based phylogenetic inference, which is novel in two respects. First, it is the only method (to our knowledge) to guarantee accuracy when knowledge about the model tree, i.e bounds on the edge lengths, is not assumed. Second, our algorithm guarantees that, with high probability, no false assertions are made. The algorithm produces a maximal forest...

On Oblique Random Forests

Abstract. In his original paper on random forests, Breiman proposed two different decision tree ensembles: one generated from “orthogonal” trees with thresholds on individual features in every split, and one from “oblique” trees separating the feature space by randomly oriented hyperplanes. In spite of a rising interest in the random forest framework, however, ensembles built from orthogonal tr...

On Euclidean distance matrices

If A is a real symmetric matrix and P is an orthogonal projection onto a hyperplane, then we derive a formula for the Moore-Penrose inverse of PAP . As an application, we obtain a formula for the MoorePenrose inverse of a Euclidean distance matrix (EDM) which generalizes formulae for the inverse of a EDM in the literature. To an invertible spherical EDM, we associate a Laplacian matrix (which w...

Lectures on Random Matrices

On Random Matrices Ii