Related papers: A complementary view on the growth of directory tr…
Phylogenetic networks are a type of directed acyclic graph that represent how a set $X$ of present-day species are descended from a common ancestor by processes of speciation and reticulate evolution. In the absence of reticulate evolution,…
The dynamic trees problem is to maintain a forest subject to edge insertions and deletions while facilitating queries such as connectivity, path weights, and subtree weights. Dynamic trees are a fundamental building block of a large number…
The ongoing explosion of genome sequence data is transforming how we reconstruct and understand the histories of biological systems. Across biological scales, from individual cells to populations and species, trees-based models provide a…
The problem of spanning trees is closely related to various interesting problems in the area of statistical physics, but determining the number of spanning trees in general networks is computationally intractable. In this paper, we perform…
We investigate the evolution rules and degree distribution properties of the Software Heritage dataset, a large-scale growing network linking software source-code versions from open-source communities. The network spans more than 40 years…
A cluster tree provides a highly-interpretable summary of a density function by representing the hierarchy of its high-density clusters. It is estimated using the empirical tree, which is the cluster tree constructed from a density…
Duplication graphs are graphs that grow by duplication of existing vertices, and are important models of biological networks, including protein-protein interaction networks and gene regulatory networks. Three models of graph growth are…
Decision trees are one of the most useful and popular methods in the machine learning toolbox. In this paper, we consider the problem of learning optimal decision trees, a combinatorial optimization problem that is challenging to solve at…
We develop a theoretical framework for the analysis of oblique decision trees, where the splits at each decision node occur at linear combinations of the covariates (as opposed to conventional tree constructions that force axis-aligned…
Retrieving relevant targets from an extremely large target set under computational limits is a common challenge for information retrieval and recommendation systems. Tree models, which formulate targets as leaves of a tree with trainable…
There has been considerable recent interest in the properties of networks, such as citation networks and the worldwide web, that grow by the addition of vertices, and a number of simple solvable models of network growth have been studied.…
We consider random partitions of the vertex set of a given finite graph that can be sampled by means of loop-erased random walks stopped at a random exponential time of parameter $q>0$. The related random blocks tend to cluster nodes…
In this work, we propose trait-based merge trees a generalization of merge trees to feature level sets, targeting the analysis of tensor field or general multi-variate data. For this, we employ the notion of traits defined in attribute…
Variable trees are a new method for the exploration of discrete multivariate data. They display nested subsets and corresponding frequencies and percentages. Manual calculation of these quantities can be laborious, especially when there are…
We propose and study a multi-scale approach to vector quantization. We develop an algorithm, dubbed reconstruction trees, inspired by decision trees. Here the objective is parsimonious reconstruction of unsupervised data, rather than…
Tree-based models are widely recognized for their interpretability and have proven effective in various application domains, particularly in high-stakes domains. However, learning decision trees (DTs) poses a significant challenge due to…
The properties of decays that take place during jet formation cannot be easily deduced from the final distribution of particles in a detector. In this work, we first simulate a system of particles with well defined masses, decay channels,…
Reinforcement learning techniques achieved human-level performance in several tasks in the last decade. However, in recent years, the need for interpretability emerged: we want to be able to understand how a system works and the reasons…
Reading comprehension models are based on recurrent neural networks that sequentially process the document tokens. As interest turns to answering more complex questions over longer documents, sequential reading of large portions of text…
The interactions among the elementary components of many complex systems can be qualitatively different. Such systems are therefore naturally described in terms of multiplex or multi-layer networks, i.e. networks where each layer stands for…