Related papers: Covering Metric Spaces by Few Trees
We analyze the finite sample mean squared error (MSE) performance of regression trees and forests in the high dimensional regime with binary features, under a sparsity constraint. We prove that if only $r$ of the $d$ features are relevant…
This paper has been withdrawn by the author, due to the fact that the main result in it has already been obtained in [1] for any c < e, see also [2] and [3]. Moreover the formula which gives the minimal vertex-cover in a tree (see the…
We study the effectiveness of subagging, or subsample aggregating, on regression trees, a popular non-parametric method in machine learning. First, we give sufficient conditions for pointwise consistency of trees. We formalize that (i) the…
We study the crossing-minimization problem in a layered graph drawing of planar-embedded rooted trees whose leaves have a given total order on the first layer, which adheres to the embedding of each individual tree. The task is then to…
Ensembles of decision trees are a useful tool for obtaining for obtaining flexible estimates of regression functions. Examples of these methods include gradient boosted decision trees, random forests, and Bayesian CART. Two potential…
In tree based adaptive mesh refinement, elements are partitioned between processes using a space filling curve. The curve establishes an ordering between all elements that derive from the same root element, the tree. When representing more…
Extreme multi-label classification (XMC) aims to identify relevant subsets from numerous labels. Among the various approaches for XMC, tree-based linear models are effective due to their superior efficiency and simplicity. However, the…
We study the problem of partitioning a set of $n$ objects in a metric space into $k$ clusters $V_1,\dots,V_k$. The quality of the clustering is measured by considering the vector of cluster costs and then minimizing some monotone symmetric…
Packing graphs is a combinatorial problem where several given graphs are being mapped into a common host graph such that every edge is used at most once. In the planar tree packing problem we are given two trees T1 and T2 on n vertices and…
We propose a procedure to build a decision tree which approximates the performance of complex machine learning models. This single approximation tree can be used to interpret and simplify the predicting pattern of random forests (RFs) and…
This paper addresses the problem of finding a representation of a subtree distance, which is an extension of the tree metric. We show that a minimal representation is uniquely determined by a given subtree distance, and give a linear time…
This article is motivated by the objective of providing a new analytically tractable and fully frequentist framework to characterize and implement regression trees while also allowing a multivariate (potentially high dimensional) response.…
Short spanning trees subject to additional constraints are important building blocks in various approximation algorithms. Especially in the context of the Traveling Salesman Problem (TSP), new techniques for finding spanning trees with…
Tree rotations (left and right) are basic local deformations allowing to transform between two unlabeled binary trees of the same size. Hence, there is a natural problem of practically finding such transformation path with low number of…
The metric space of phylogenetic trees defined by Billera, Holmes, and Vogtmann, which we refer to as BHV space, provides a natural geometric setting for describing collections of trees on the same set of taxa. However, it is sometimes…
We present convincing empirical evidence for an effective and general strategy for building accurate small models. Such models are attractive for interpretability and also find use in resource-constrained environments. The strategy is to…
Cartesian tree pattern matching consists of finding all the factors of a text that have the same Cartesian tree than a given pattern. There already exist theoretical and practical solutions for the exact case. In this paper, we propose the…
The (axis-parallel) stabbing number of a given set of line segments is the maximum number of segments that can be intersected by any one (axis-parallel) line. This paper deals with finding perfect matchings, spanning trees, or…
Trees have long been used as a graphical representation of species relationships. However complex evolutionary events, such as genetic reassortments or hybrid speciations which occur commonly in viruses, bacteria and plants, do not fit into…
Neuroscientific data analysis has classically involved methods for statistical signal and image processing, drawing on linear algebra and stochastic process theory. However, digitized neuroanatomical data sets containing labelled neurons,…