Related papers: A recursive algorithm for trees and forests
A tree with at most $k$ leaves is called a $k$-ended tree. A spanning 2-ended tree is a Hamilton path. A Hamilton cycle can be considered as a spanning 1-ended tree. The earliest result concerning spanning trees with few leaves states that…
This paper deals with computation trees over an arbitrary structure consisting of a set along with collections of functions and predicates that are defined on it. It is devoted to the comparative analysis of three parameters of problems…
Poly-trees are singly connected causal networks in which variables may arise from multiple causes. This paper develops a method of recovering ply-trees from empirically measured probability distributions of pairs of variables. The method…
We consider three bivariate polynomial invariants $P$, $A$, and $S$ for rooted trees, as well as a trivariate polynomial invariant $M$. These invariants are motivated by random destruction processes such as the random cutting model or site…
In "Square partitions and Catalan numbers" (arXiv0912.4983), Bennett et al. presented a recursive algorithm to create a family of partitions from one or several partitions. They were mainly interested in the cases when we begin with a…
We introduce some natural families of distributions on rooted binary ranked plane trees with a view toward unifying ideas from various fields, including macroevolution, epidemiology, computational group theory, search algorithms and other…
We present a computational model to reconstruct trees of ancestors for animals with sexual reproduction. Through a recursive algorithm combined with a random number generator, it is possible to reproduce the number of ancestors for each…
Bayesian Decision Trees are known for their probabilistic interpretability. However, their construction can sometimes be costly. In this article we present a general Bayesian Decision Tree algorithm applicable to both regression and…
The forest-of-octrees approach to parallel adaptive mesh refinement and coarsening (AMR) has recently been demonstrated in the context of a number of large-scale PDE-based applications. Although linear octrees, which store only leaf…
Let $T$ be a weighted tree. The weight of a subtree $T_1$ of $T$ is defined as the product of weights of vertices and edges of $T_1$. We obtain a linear-time algorithm to count the sum of weights of subtrees of $T$. As applications, we…
Let T be a (not necessarily positive) weighted tree with n leaves numbered by the set {1,...,n}. Define the k-weights of the tree D_{i_1,....,i_k}(T) as the sum of the lengths of the edges of the minimal subtree connecting i_1,....,i_k. We…
Decision tree learning is increasingly being used for pointwise inference. Important applications include causal heterogenous treatment effects and dynamic policy decisions, as well as conditional quantile regression and design of…
We present here a new and universal approach for the study of random and/or trees, unifying in one framework many different models, including some novel ones not yet understood in the literature. An and/or tree is a Boolean expression…
We enumerate injectively $k$-colored rooted forests with a given number of vertices of each color and a given sequence of root colors. We obtain from this result some new multi-parameter distributions of Fuss-Catalan numbers. As an…
We prime-encode the natural numbers via recursive factorisation, iterated to the exponents, generating a corpus of planar rooted trees equivalently represented as Dyck words. This forms a deterministic text endowed with internal rules.…
In order to speed-up classification models when facing a large number of categories, one usual approach consists in organizing the categories in a particular structure, this structure being then used as a way to speed-up the prediction…
Phylogenetic networks generalize phylogenetic trees by allowing the modelization of events of reticulate evolution. Among the different kinds of phylogenetic networks that have been proposed in the literature, the subclass of binary…
Using the Lagrange inversion formula, $t$-ary trees are enumerated with respect to edge type (left, middle, right for ternary trees).
We consider finding a counterfactual explanation for a classification or regression forest, such as a random forest. This requires solving an optimization problem to find the closest input instance to a given instance for which the forest…
Pairwise ordered tree alignment are combinatorial objects that appear in RNA secondary structure comparison. However, the usual representation of tree alignments as supertrees is ambiguous, i.e. two distinct supertrees may induce identical…