Related papers: Patterns in treeshelves
There are several good reasons you might want to read about uniform spanning trees, one being that spanning trees are useful combinatorial objects. Not only are they fundamental in algebraic graph theory and combinatorial geometry, but they…
The observation that some subgraphs, called motifs, appear more often in real networks than in their randomized counterparts has attracted much attention in the scientific community. In the prevalent approach the detection of motifs is…
In biology, a phylogenetic tree is a tool to represent the evolutionary relationship between species. Unfortunately, the classical Schr\"oder tree model is not adapted to take into account the chronology between the branching nodes. In…
We study power-set operations on classes of trees and tree algebras. Our main result consists of a distributive law between the tree monad and the upwards-closed power-set monad, in the case where all trees are assumed to be linear. For…
We introduce the zip tree, a form of randomized binary search tree that integrates previous ideas into one practical, performant, and pleasant-to-implement package. A zip tree is a binary search tree in which each node has a numeric rank…
Ensembles of decision trees perform well on many problems, but are not interpretable. In contrast to existing approaches in interpretability that focus on explaining relationships between features and predictions, we propose an alternative…
We consider supervised learning with random decision trees, where the tree construction is completely random. The method is popularly used and works well in practice despite the simplicity of the setting, but its statistical mechanism is…
In many applications of clustering (for example, ontologies or clusterings of animal or plant species), hierarchical clusterings are more descriptive than a flat clustering. A hierarchical clustering over $n$ elements is represented by a…
Tree-child networks are one of the most prominent network classes for modeling evolutionary processes which contain reticulation events. Several recent studies have addressed counting questions for {\it bicombining tree-child networks}…
We consider the problem of constructing an an optimal-weight tree from the 3*(n choose 4) weighted quartet topologies on n objects, where optimality means that the summed weight of the embedded quartet topologiesis optimal (so it can be the…
Robotic systems for household object rearrangement often rely on latent preference models inferred from human demonstrations. While effective at prediction, these models offer limited insight into the interpretable factors that guide human…
We develop a theory of sets with distributive products (called shelves and multi-shelves) and of their homology. We relate the shelf homology to the rack and quandle homology.
In data analysis, latent variables play a central role because they help provide powerful insights into a wide variety of phenomena, ranging from biological to human sciences. The latent tree model, a particular type of probabilistic…
We study a class of combinatorial objects that we call "decorated trees". These consist of vertices, arrows and edges, where each edge is decorated by two integers (one near each of its endpoints), each arrow is decorated by an integer, and…
The rank (also known as protection number or leaf-height) of a vertex in a rooted tree is the minimum distance between the vertex and any of its leaf descendants. We consider the sum of ranks over all vertices (known as the security) in…
A new family of tree models is proposed, which we call "differential trees." A differential tree model is constructed from multiple data sets and aims to detect distributional differences between them. The new methodology differs from the…
The hierarchical and recursive expressive capability of rooted trees is applicable to represent statistical models in various areas, such as data compression, image processing, and machine learning. On the other hand, such hierarchical…
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…
The problem of selecting a small, yet high quality subset of patterns from a larger collection of itemsets has recently attracted lot of research. Here we discuss an approach to this problem using the notion of decomposable families of…
Given a graph, we can form a spanning forest by first sorting the edges in some order, and then only keep edges incident to a vertex which is not incident to any previous edge. The resulting forest is dependent on the ordering of the edges,…