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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…
We introduce a new class of tree-based models, P-Trees, for analyzing (unbalanced) panel of individual asset returns, generalizing high-dimensional sorting with economic guidance and interpretability. Under the mean-variance efficient…
D. Wilson~\cite{[Wi]} in the 1990's described a simple and efficient algorithm based on loop-erased random walks to sample uniform spanning trees and more generally weighted trees or forests spanning a given graph. This algorithm provides a…
In the last few years, graph convolutional networks (GCN) have become a popular research direction in the machine learning community to tackle NP-hard combinatorial optimization problems (COPs) defined on graphs. While the obtained results…
Survival analysis concerns the task of predicting the time until an event occurs. Often used in the medical field, survival analysis deals with incomplete (i.e., censored) data, for instance, from patients who did not experience the event…
In molecular phylogeny, relationships among organisms are reconstructed using DNA or protein sequences and are displayed as trees. A linear increase in the number of sequences results in an exponential increase of possible trees. Thus,…
Random forests on the one hand, and neural networks on the other hand, have met great success in the machine learning community for their predictive performance. Combinations of both have been proposed in the literature, notably leading to…
Combining machine learning with econometric analysis is becoming increasingly prevalent in both research and practice. A common empirical strategy involves the application of predictive modeling techniques to 'mine' variables of interest…
This paper characterizes and discusses devolutionary genetic algorithms and evaluates their performances in solving the minimum labeling Steiner tree (MLST) problem. We define devolutionary algorithms as the process of reaching a feasible…
Tree ensembles are flexible predictive models that can capture relevant variables and to some extent their interactions in a compact and interpretable manner. Most algorithms for obtaining tree ensembles are based on versions of boosting or…
Topologically constrained genome-like polymers often double-fold into tree-like configurations, which can be modelled on the level of folded (ring) polymers or on the level of the underlying random trees. For both descriptions, we have…
Phylogenetic trees are used to model evolution: leaves are labelled to represent contemporary species ("taxa") and interior vertices represent extinct ancestors. Informally, convex characters are measurements on the contemporary species in…
The stability and ability of an ecosystem to withstand climate change is directly linked to its biodiversity. Dead trees are a key indicator of overall forest health, housing one-third of forest ecosystem biodiversity, and constitute 8%of…
Phylogenetic networks generalise phylogenetic trees and allow for the accurate representation of the evolutionary history of a set of present-day species whose past includes reticulate events such as hybridisation and lateral gene transfer.…
We consider the probability that a spanning tree chosen uniformly at random from a graph can be partitioned into a fixed number $k$ of trees of equal size by removing $k-1$ edges. In that case, the spanning tree is called {\em splittable}.…
One strategy for reconstruction of phylogenetic networks is to solve the phylogenetic network problem, which involves inferring phylogenetic trees first and subsequently computing the smallest phylogenetic network that displays all the…
The aim of this chapter is to provide an adequate graph theoretic framework for the description of periodic bifurcations which have recently been discovered in descendant trees of finite p-groups. The graph theoretic concepts of rooted…
Color-constrained subgraph problems are those where we are given an edge-colored (directed or undirected) graph and the task is to find a specific type of subgraph, like a spanning tree, an arborescence, a single-source shortest path tree,…
Estimating phylogenetic trees is an important problem in evolutionary biology, environmental policy and medicine. Although trees are estimated, their uncertainties are discarded by mathematicians working in tree space. Here we explicitly…
Daily internet communication relies heavily on tree-structured graphs, embodied by popular data formats such as XML and JSON. However, many recent generative (probabilistic) models utilize neural networks to learn a probability distribution…