Related papers: Finding the seed of uniform attachment trees
In phylogenetics, a central problem is to infer the evolutionary relationships between a set of species $X$; these relationships are often depicted via a phylogenetic tree -- a tree having its leaves univocally labeled by elements of $X$…
Existing ordinal trees and random forests typically use scores that are assigned to the ordered categories, which implies that a higher scale level is used. Versions of ordinal trees are proposed that take the scale level seriously and…
We study three different kinds of embeddings of tree patterns: weakly-injective, ancestor-preserving, and lca-preserving. While each of them is often referred to as injective embedding, they form a proper hierarchy and their computational…
The main goal of this paper is to provide an algorithm for the random sampling of Butcher trees and the probabilistic numerical solution of ordinary differential equations (ODEs). This approach complements and simplifies a recent approach…
We study various types of consistency of honest decision trees and random forests in the regression setting. In contrast to related literature, our proofs are elementary and follow the classical arguments used for smoothing methods. Under…
A weighted recursive tree is an evolving tree in which vertices are assigned random vertex-weights and new vertices connect to a predecessor with a probability proportional to its weight. Here, we study the maximum degree and near-maximum…
A chief problem in phylogenetics and database theory is the computation of a maximum consistent tree from a set of rooted or unrooted trees. A standard input are triplets, rooted binary trees on three leaves, or quartets, unrooted binary…
The size of the largest common subtree (maximum agreement subtree) of two independent uniform random binary trees on $n$ leaves is known to be between orders $n^{1/8}$ and $n^{1/2}$. By a construction based on recursive splitting and…
We study upward planar straight-line embeddings (UPSE) of directed trees on given point sets. The given point set $S$ has size at least the number of vertices in the tree. For the special case where the tree is a path $P$ we show that: (a)…
The reconstruction of a central tendency `species tree' from a large number of conflicting gene trees is a central problem in systematic biology. Moreover, it becomes particularly problematic when taxon coverage is patchy, so that not all…
We present a study of several generic tree search techniques applied to the Sequential Ordering Problem. This study enables us to propose a simple and competitive tree search algorithm. It consists of an iterative Beam Search algorithm that…
We study the problem of learning a node-labeled tree given independent traces from an appropriately defined deletion channel. This problem, tree trace reconstruction, generalizes string trace reconstruction, which corresponds to the tree…
The recursive and hierarchical structure of full rooted trees is applicable to represent statistical models in various areas, such as data compression, image processing, and machine learning. In most of these cases, the full rooted tree is…
A uniform $k$-{\sc dag} generalizes the uniform random recursive tree by picking $k$ parents uniformly at random from the existing nodes. It starts with $k$ ''roots''. Each of the $k$ roots is assigned a bit. These bits are propagated by a…
Random forests construct each tree with a different, randomised representation of the feature space. Their uniform voting cannot correct errors in regions where trees with incorrect representations probabilistically outnumber correct ones,…
In this paper we offer a new perspective on the well established agglomerative clustering algorithm, focusing on recovery of hierarchical structure. We recommend a simple variant of the standard algorithm, in which clusters are merged by…
The Aldous--Broder algorithm provides a way of sampling a uniformly random spanning tree for finite connected graphs using simple random walk. Namely, start a simple random walk on a connected graph and stop at the cover time. The tree…
Random Forest is an ensemble of decision trees based on the bagging and random subspace concepts. As suggested by Breiman, the strength of unstable learners and the diversity among them are the ensemble models' core strength. In this paper,…
Random forests are ensemble methods which grow trees as base learners and combine their predictions by averaging. Random forests are known for their good practical performance, particularly in high dimensional set-tings. On the theoretical…
We present a new algorithm for generating a uniformly random spanning tree in an undirected graph. Our algorithm samples such a tree in expected $\tilde{O}(m^{4/3})$ time. This improves over the best previously known bound of…