Related papers: Probability Distribution on Full Rooted Trees
This paper presents a new approach for trees-based regression, such as simple regression tree, random forest and gradient boosting, in settings involving correlated data. We show the problems that arise when implementing standard…
We show that an algorithmic construction of sequences of recursive trees leads to a direct proof of the convergence of random recursive trees in an associated Doob-Martin compactification; it also gives a representation of the limit in…
A large number of explicit estimators are proposed in this paper for loss rate estimation in a network of the tree topology. All of the estimators are proved to be unbiased and consistent instead of asymptotic unbiased as that obtained in…
Tree ensembles, such as random forests and boosted trees, are renowned for their high prediction performance. However, their interpretability is critically limited due to the enormous complexity. In this study, we present a method to make a…
It can be important in Bayesian analyses of complex models to construct informative prior distributions which reflect knowledge external to the data at hand. Nevertheless, how much prior information an analyst can elicit from an expert will…
The paper presents Maximal Ellipsoid Backward Reachable Trees MAXELLIPSOID BRT, which is a multi-query algorithm for planning of dynamic systems under stochastic motion uncertainty and constraints on the control input. In contrast to…
We consider nonparametric Bayesian estimation of a probability density $p$ based on a random sample of size $n$ from this density using a hierarchical prior. The prior consists, for instance, of prior weights on the regularity of the…
Supertree construction is the process by which a set of phylogenetic trees, each on a subset of the overall set X of species, is combined into a tree on the full set S. The traditional use of supertree methods is the assembly of a large…
Comparative analyses of phylogenetic trees typically require identical taxon sets, however, in practice, trees often include distinct but overlapping taxa. Pruning non-shared leaves discards phylogenetic signal, whereas tree completion can…
The Robinson-Foulds (RF) distance is by far the most widely used measure of dissimilarity between trees. Although the distribution of these distances has been investigated for twenty years, an algorithm that is explicitly polynomial time…
The use of machine learning algorithms in finance, medicine, and criminal justice can deeply impact human lives. As a consequence, research into interpretable machine learning has rapidly grown in an attempt to better control and fix…
We consider linear preferential attachment trees, and show that they can be regarded as random split trees in the sense of Devroye (1999), although with infinite potential branching. In particular, this applies to the random recursive tree…
Probabilistic regression models the entire predictive distribution of a response variable, offering richer insights than classical point estimates and directly allowing for uncertainty quantification. While diffusion-based generative models…
Given a solution to a recursive distributional equation, a natural (and non-trivial) question is whether the corresponding recursive tree process is endogenous. That is, whether the random environment almost surely defines the tree process.…
We analyse a maximum-likelihood approach for combining phylogenetic trees into a larger `supertree'. This is based on a simple exponential model of phylogenetic error, which ensures that ML supertrees have a simple combinatorial description…
Algorithms for binary classification based on adaptive tree partitioning are formulated and analyzed for both their risk performance and their friendliness to numerical implementation. The algorithms can be viewed as generating a set…
Regression trees are a popular machine learning algorithm that fit piecewise constant models by recursively partitioning the predictor space. This paper focuses on statistical inference for a data-dependent model obtained from a fitted…
We investigate approximating joint distributions of random processes with causal dependence tree distributions. Such distributions are particularly useful in providing parsimonious representation when there exists causal dynamics among…
This study is dedicated to precise distributional analyses of the height of non-plane unlabelled binary trees ("Otter trees"), when trees of a given size are taken with equal likelihood. The height of a rooted tree of size $n$ is proved to…
In this paper, we redesign and simplify an algorithm due to Remy et al. for the generation of rooted planar trees that satisfies a given partition of degrees. This new version is now optimal in terms of random bit complexity, up to a…