Related papers: Multiple isolation of nodes in recursive trees

In the critical beta-splitting model of a random $n$-leaf rooted tree, clades are recursively (from the root) split into sub-clades, and a clade of $m$ leaves is split into sub-clades containing $i$ and $m-i$ leaves with probabilities…

We investigate characteristics of random split trees introduced by Devroye; split trees include for example binary search trees, $m$-ary search trees, quadtrees, median of $(2k+1)$-trees, simplex trees, tries and digital search trees. More…

The problem of community detection in networks is usually formulated as finding a single partition of the network into some "correct" number of communities. We argue that it is more interpretable and in some regimes more accurate to…

Decision trees are widely used for non-linear modeling, as they capture interactions between predictors while producing inherently interpretable models. Despite their popularity, performing inference on the non-linear fit remains largely…

We provide a local probabilistic description of the limiting statistics of large preferential attachment trees in terms of the ordinary degree (number of neighbors) but augmented with information on leafdegree (number of neighbors that are…

Reductions---rules that reduce input size while maintaining the ability to compute an optimal solution---are critical for developing efficient maximum independent set algorithms in both theory and practice. While several simple reductions…

In this paper we investigate formal verification of extracted rules for Neural Networks under a complexity theoretic point of view. A rule is a global property or a pattern concerning a large portion of the input space of a network. These…

Centrality metrics play a crucial role in network analysis, while the choice of specific measures significantly influences the accuracy of conclusions as each measure represents a unique concept of node importance. Among over 400 proposed…

In phylogenetics, tree-based networks are used to model and visualize the evolutionary history of species where reticulate events such as horizontal gene transfer have occurred. Formally, a tree-based network $N$ consists of a phylogenetic…

Decision trees and their ensembles are popular in machine learning as easy-to-understand models. Several techniques have been proposed in the literature for learning tree-based classifiers, with different techniques working well for data…

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 the broadcasting problem when the underlying tree is a random recursive tree. The root of the tree has a random bit value assigned. Every other vertex has the same bit value as its parent with probability $1-q$ and the opposite…

In this paper, Bayesian based aggregation of decision trees in an ensemble (decision forest) is investigated. The focus is laid on multi-class classification with number of samples significantly skewed toward one of the classes. The…

Inspired by [4] we present a new algorithm for uniformly random generation of ordered trees in which all occuring outdegrees can be specified by a given sequence of numbers. The method can be used for random generation of binary or n-ary…

The main goal of this paper is to describe a new pruning method for solving decision trees and game trees. The pruning method for decision trees suggests a slight variant of decision trees that we call scenario trees. In scenario trees, we…

As a generalization of random recursive trees and preferential attachment trees, we consider random recursive metric spaces. These spaces are constructed from random blocks, each a metric space equipped with a probability measure,…

Random forests are decision tree ensembles that can be used to solve a variety of machine learning problems. However, as the number of trees and their individual size can be large, their decision making process is often incomprehensible. In…

In this paper, we focus on the prediction phase of a random forest and study the problem of representing a bag of decision trees using a smaller bag of decision trees, where we only consider binary decision problems on the binary domain and…

Classification and Regression Trees (CARTs) are off-the-shelf techniques in modern Statistics and Machine Learning. CARTs are traditionally built by means of a greedy procedure, sequentially deciding the splitting predictor variable(s) and…

Tree search algorithms, such as branch-and-bound, are the most widely used tools for solving combinatorial and nonconvex problems. For example, they are the foremost method for solving (mixed) integer programs and constraint satisfaction…