相关论文: The performance guarantee of randomized perfect vo…

This paper presents a brand new nonparametric density estimation strategy named the best-scored random forest density estimation whose effectiveness is supported by both solid theoretical analysis and significant experimental performance.…

Selecting from or ranking a set of candidates variables in terms of their capacity for predicting an outcome of interest is an important task in many scientific fields. A variety of methods for variable selection and ranking have been…

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…

Within machine learning, the supervised learning field aims at modeling the input-output relationship of a system, from past observations of its behavior. Decision trees characterize the input-output relationship through a series of nested…

We study properties of the harmonic measure of balls in typical large discrete trees. For a ball of radius $n$ centered at the root, we prove that, although the size of the boundary is of order $n$, most of the harmonic measure is supported…

Random Forest is an ensemble of decision trees based on the bagging and random subspace concepts. As suggested by Breiman, the strength of unstable learners and the diversity among them are the ensemble models' core strength. In this paper,…

We consider random dynamical systems generated by a special class of Volterra quadratic stochastic operators on the simplex $S^{m-1}$. We prove that in contrast to the deterministic set-up the trajectories of the random dynamical system…

This work develops formal statistical inference procedures for machine learning ensemble methods. Ensemble methods based on bootstrapping, such as bagging and random forests, have improved the predictive accuracy of individual trees, but…

We consider the stochastic geometry model where the location of each node is a random point in a given metric space, or the existence of each node is uncertain. We study the problems of computing the expected lengths of several…

We prove that a random labeled (unlabeled) tree is balanced. We also prove that random labeled and unlabeled trees are strongly $k$-balanced for any $k\geq 3$.

Randomized search algorithms for hard combinatorial problems exhibit a large variability of performances. We study the different types of rare events which occur in such out-of-equilibrium stochastic processes and we show how they cooperate…

Tree ensembles (TEs) find a multitude of practical applications. They represent one of the most general and accurate classes of machine learning methods. While they are typically quite concise in representation, their operation remains…

Classification and Regression Tree (CART), Random Forest (RF) and Gradient Boosting Tree (GBT) are probably the most popular set of statistical learning methods. However, their statistical consistency can only be proved under very…

A simple and computationally efficient scheme for tree-structured vector quantization is presented. Unlike previous methods, its quantization error depends only on the intrinsic dimension of the data distribution, rather than the apparent…

Two distinct specifications of single peakedness as currently met in the relevant literature are singled out and discussed. Then, it is shown that, under both of those specifications, a voting rule as defined on a bounded distributive…

Connected acyclic graphs (trees) are data objects that hierarchically organize categories. Collections of trees arise in a diverse variety of fields, including evolutionary biology, public health, machine learning, social sciences and…

A quota mechanism, such as a mandatory grading curve, links together multiple decisions. We analyze the performance of quota mechanisms when the number of linked decisions is finite and the designer has imperfect knowledge of the type…

Single-level density-based approach has long been widely acknowledged to be a conceptually and mathematically convincing clustering method. In this paper, we propose an algorithm called "best-scored clustering forest" that can obtain the…

The number of trees T in the random forest (RF) algorithm for supervised learning has to be set by the user. It is controversial whether T should simply be set to the largest computationally manageable value or whether a smaller T may in…

We present a new algorithm for generating a uniformly random spanning tree in an undirected graph. Our algorithm samples such a tree in expected $\tilde{O}(m^{4/3})$ time. This improves over the best previously known bound of…