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In recent years, dynamically growing data and incrementally growing number of classes pose new challenges to large-scale data classification research. Most traditional methods struggle to balance the precision and computational burden when…
A Yule tree is the result of a branching process with constant birth and death rates. Such a process serves as an instructive null model of many empirical systems, for instance, the evolution of species leading to a phylogenetic tree.…
We prove non-asymptotic stretched exponential tail bounds on the height of a randomly sampled node in a random combinatorial tree, which we use to prove bounds on the heights and widths of random trees from a variety of models. Our results…
We destroy a finite tree of size $n$ by cutting its edges one after the other and in uniform random order. Informally, the associated cut-tree describes the genealogy of the connected components created by this destruction process. We…
We consider linear preferential attachment trees which are specific scale-free trees also known as (random) plane-oriented recursive trees. Starting with a linear preferential attachment tree of size $n$ we show that repeatedly applying a…
To each sequence $(a_n)$ of positive real numbers we associate a growing sequence $(T_n)$ of continuous trees built recursively by gluing at step $n$ a segment of length $a_n$ on a uniform point of the pre-existing tree, starting from a…
We study a general model of recursive trees where vertices are equipped with independent weights and at each time-step a vertex is sampled with probability proportional to its fitness function (a function of its weight and degree) and…
Respiration measurements of whole tree plants have been reported that give evidence that the relative per volume/mass unit respiration decreases with increase of tree body size. In this study, based on the available data published a…
Random Forests (RF) is a popular machine learning method for classification and regression problems. It involves a bagging application to decision tree models. One of the primary advantages of the Random Forests model is the reduction in…
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 consider three probability measures on subsets of edges of a given finite graph $G$, namely those which govern, respectively, a uniform forest, a uniform spanning tree, and a uniform connected subgraph. A conjecture concerning the…
We consider a class of reinforcement processes, called WARMs, on tree graphs. These processes involve a parameter $\alpha$ which governs the strength of the reinforcement, and a collection of Poisson processes indexed by the vertices of the…
The properties of scale-free random trees are investigated using both preconditioning on non-extinction and fixed size averages, in order to study the thermodynamic limit. The scaling form of volume probability is found, the connectivity…
Accurate tree height estimation is vital for ecological monitoring and biomass assessment. We apply quantile regression to existing tree height estimation models based on satellite data to incorporate uncertainty quantification. Most…
In this work, we study how to maintain a forest of arborescences of maximum arc cardinality under arc insertions while minimizing recourse -- the total number of arcs changed in the maintained solution. This problem is the "arborescence…
We present a link-by-link rule-based method for constructing all members of the ensemble of spanning trees for any recursively generated, finitely articulated graph, such as the DGM net. The recursions allow for many large-scale properties…
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…
Random forests are a very effective and commonly used statistical method, but their full theoretical analysis is still an open problem. As a first step, simplified models such as purely random forests have been introduced, in order to shed…
We propose a generalized model for uniform recursive tree (URT) by introducing an imperfect growth process, which may generate disconnected components (clusters). The model undergoes an interesting phase transition from a singly connected…
Ensemble learning methods are designed to benefit from multiple learning algorithms for better predictive performance. The tradeoff of this improved performance is slower speed and larger size of ensemble learning systems compared to single…