相关论文: Random trees between two walls: Exact partition fu…
We develop some theory of spinal decompositions of discrete and continuous fragmentation trees. Specifically, we consider a coarse and a fine spinal integer partition derived from spinal tree decompositions. We prove that for a…
Given a set S of n \geq d points in general position in R^d, a random hyperplane split is obtained by sampling d points uniformly at random without replacement from S and splitting based on their affine hull. A random hyperplane search tree…
A decision tree is commonly restricted to use a single hyperplane to split the covariate space at each of its internal nodes. It often requires a large number of nodes to achieve high accuracy, hurting its interpretability. In this paper,…
Tackling simulation optimization problems with non-convex objective functions remains a fundamental challenge in operations research. In this paper, we propose a class of random search algorithms, called Regular Tree Search, which…
The k-d tree was one of the first spatial data structures proposed for nearest neighbor search. Its efficacy is diminished in high-dimensional spaces, but several variants, with randomization and overlapping cells, have proved to be…
We study the graph structure of large random dissections of polygons sampled according to Boltzmann weights, which encompasses the case of uniform dissections or uniform $p$-angulations. As their number of vertices $n$ goes to infinity, we…
The basic object we consider is a certain model of continuum random tree, called the stable tree. We construct a fragmentation process $(F^-(t), t>=0)$ out of this tree by removing the vertices located under height $t$. Thanks to a…
Random survival forest and survival trees are popular models in statistics and machine learning. However, there is a lack of general understanding regarding consistency, splitting rules and influence of the censoring mechanism. In this…
We propose a tree-based algorithm for classification and regression problems in the context of functional data analysis, which allows to leverage representation learning and multiple splitting rules at the node level, reducing…
D. Wilson~\cite{[Wi]} in the 1990's described a simple and efficient algorithm based on loop-erased random walks to sample uniform spanning trees and more generally weighted trees or forests spanning a given graph. This algorithm provides a…
Tree-based priors for probability distributions are usually specified using a predetermined, data-independent collection of candidate recursive partitions of the sample space. To characterize an unknown target density in detail over the…
Given a tree of weighted vertices, it is sometimes possible to break the tree into two equally-weighted subtrees within an allowable error. We give a fast algorithm that finds an edge which breaks the tree into equal-weight components or…
We determine the limit of the expected value and the variance of the protection number of the root in simply generated trees, in P\'olya trees, and in unlabelled non-plane binary trees, when the number of vertices tends to infinity.…
In tree based adaptive mesh refinement, elements are partitioned between processes using a space filling curve. The curve establishes an ordering between all elements that derive from the same root element, the tree. When representing more…
We study two models of discrete height functions, that is, models of random integer-valued functions on the vertices of a tree. First, we consider the random homomorphism model, in which neighbours must have a height difference of exactly…
We study a model of random $\mathcal{R}$-enriched trees that is based on weights on the $\mathcal{R}$-structures and allows for a unified treatment of a large family of random discrete structures. We establish distributional limits…
We propose a novel algorithm for optimizing multivariate linear threshold functions as split functions of decision trees to create improved Random Forest classifiers. Standard tree induction methods resort to sampling and exhaustive search…
Random forests have become an established tool for classification and regression, in particular in high-dimensional settings and in the presence of complex predictor-response relationships. For bounded outcome variables restricted to the…
Treemaps are a popular technique to visualize hierarchical data. The input is a weighted tree $\tree$ where the weight of each node is the sum of the weights of its children. A treemap for $\tree$ is a hierarchical partition of a rectangle…
Aerial image segmentation is the basis for applications such as automatically creating maps or tracking deforestation. In true orthophotos, which are often used in these applications, many objects and regions can be approximated well by…