Finding interactions between variables in large and high-dimensional data sets is often a serious computational challenge. Most approaches build up interaction sets incrementally, adding variables in a greedy fashion. The drawback is that potentially informative high-order interactions may be overlooked. Here, we propose an alternative approach for classification problems with binary predictor ...

Abstract. A hyperplane search tree is a binary tree used to store a set S of n d-dimensional data points. In a random hyperplane search tree for S, the root represents a hyperplane defined by d data points drawn uniformly at random from S. The remaining data points are split by the hyperplane, and the definition is used recursively on each subset. We assume that the data are points in general p...

Let us consider the probability space Ifi(n, p) consisting of all graphs on n labeled vertices where each edge occurs with probability p =1q, independently of all other edges . The aim of this note is to find such natural numbers which are likely to occur as orders of maximal induced trees contained in a graph G E 19(n, p) when 0 < p < 1 is fixed . By a maximal induced tree we mean an induced t...

We give a new, simple construction of the α-stable tree for α ∈ (1, 2]. We obtain it as the closure of an increasing sequence of R-trees inductively built by gluing together line-segments one by one. The lengths of these line-segments are related to the the increments of an increasing R+-valued Markov chain. For α = 2, we recover Aldous’ line-breaking construction of the Brownian continuum rand...

We study protected nodes in various classes of random rooted trees by putting them in the general context of fringe subtrees introduced by Aldous (1991). Several types of random trees are considered: simply generated trees (or conditioned Galton– Watson trees), which includes several cases treated separately by other authors, binary search trees and random recursive trees. This gives unified an...