Related papers: Probability Distribution on Rooted Trees

We propose Partition Tree, a novel tree-based framework for conditional density estimation over general outcome spaces that supports both continuous and categorical variables within a unified formulation. Our approach models conditional…

A compositional tree refers to a tree structure on a set of random variables where each random variable is a node and composition occurs at each non-leaf node of the tree. As a generalization of compositional data, compositional trees…

There has been a lot of recent work on Bayesian methods for reinforcement learning exhibiting near-optimal online performance. The main obstacle facing such methods is that in most problems of interest, the optimal solution involves…

We investigate the statistics of trees grown from some initial tree by attaching links to preexisting vertices, with attachment probabilities depending only on the valence of these vertices. We consider the asymptotic mass distribution that…

We study the influence of the seed in random trees grown according to the uniform attachment model, also known as uniform random recursive trees. We show that different seeds lead to different distributions of limiting trees from a total…

Given i.i.d. data from an unknown distribution, we consider the problem of predicting future items. An adaptive way to estimate the probability density is to recursively subdivide the domain to an appropriate data-dependent granularity. A…

Tree-based ensemble methods, as Random Forests and Gradient Boosted Trees, have been successfully used for regression in many applications and research studies. Furthermore, these methods have been extended in order to deal with uncertainty…

Probabilistic, hierarchically coherent forecasting is a key problem in many practical forecasting applications -- the goal is to obtain coherent probabilistic predictions for a large number of time series arranged in a pre-specified tree…

We present a detailed analysis of the class of regression decision tree algorithms which employ a regulized piecewise-linear node-splitting criterion and have regularized linear models at the leaves. From a theoretic standpoint, based on…

Hash codes are a very efficient data representation needed to be able to cope with the ever growing amounts of data. We introduce a random forest semantic hashing scheme with information-theoretic code aggregation, showing for the first…

Probability trees are one of the simplest models of causal generative processes. They possess clean semantics and -- unlike causal Bayesian networks -- they can represent context-specific causal dependencies, which are necessary for e.g.…

Bayesian model selection is premised on the assumption that the data are generated from one of the postulated models. However, in many applications, all of these models are incorrect (that is, there is misspecification). When the models are…

We study the convergence of the predictive surface of regression trees and forests. To support our analysis we introduce a notion of adaptive concentration for regression trees. This approach breaks tree training into a model selection…

The goal of these lectures is to review some mathematical aspects of random tree models used in evolutionary biology to model gene trees or species trees. We start with stochastic models of tree shapes (finite trees without edge lengths),…

Trees or rooted trees have been generously studied in the literature. A forest is a set of trees or rooted trees. Here we give recurrence relations between the number of some kind of rooted forest with $k$ roots and that with $k+1$ roots on…

For a pair consisting of a gene tree and a species tree, the ancestral configurations at an internal node of the species tree are the distinct sets of gene lineages that can be present at that node. Ancestral configurations appear in…

We introduce an extension of the P\'olya tree approach for constructing distributions on the space of probability measures. By using optional stopping and optional choice of splitting variables, the construction gives rise to random…

Decision trees are a popular family of models due to their attractive properties such as interpretability and ability to handle heterogeneous data. Concurrently, missing data is a prevalent occurrence that hinders performance of machine…

We analyze variational inference for highly symmetric graphical models such as those arising from first-order probabilistic models. We first show that for these graphical models, the tree-reweighted variational objective lends itself to a…

We consider a distributed detection system with communication constraints, where several nodes are arranged in an arbitrary tree topology, under the assumption of conditionally independent observations. We propose a cyclic design procedure…