Related papers: Rises in forests of binary shrubs
When using machine learning for imbalanced binary classification problems, it is common to subsample the majority class to create a (more) balanced training dataset. This biases the model's predictions because the model learns from data…
In this paper we present new results on the enumeration of parking functions and labeled forests. We introduce new statistics on parking functions, which are then extended to labeled forests via bijective correspondences. We determine the…
Two algorithms proposed by Leo Breiman : CART trees (Classification And Regression Trees for) introduced in the first half of the 80s and random forests emerged, meanwhile, in the early 2000s, are the subject of this article. The goal is to…
The main goal of this paper is to describe a data structure called binary join trees that are useful in computing multiple marginals efficiently using the Shenoy-Shafer architecture. We define binary join trees, describe their utility, and…
We provide a fundamental result for bucket increasing trees, which gives a complete characterization of all families of bucket increasing trees that can be generated by a tree evolution process. We also provide several equivalent…
Due to the steadily increasing relevance of machine learning for practical applications, many of which are coming with safety requirements, the notion of uncertainty has received increasing attention in machine learning research in the last…
We give combinatorial descriptions of two stochastic growth models for series-parallel networks introduced by Hosam Mahmoud by encoding the growth process via recursive tree structures. Using decompositions of the tree structures and…
The distribution of distances in the star graph $ST_n$, ($1<n\in\Z$), is established, and subsequently a threaded binary tree is obtained that realizes an orientation of $ST_n$ whose levels are given by the distances to the identity…
We study the statistics of height and balanced height in the binary search tree problem in computer science. The search tree problem is first mapped to a fragmentation problem which is then further mapped to a modified directed polymer…
In analogy to other concepts of a similar nature, we define the inducibility of a rooted binary tree. Given a fixed rooted binary tree $B$ with $k$ leaves, we let $\gamma(B,T)$ be the proportion of all subsets of $k$ leaves in $T$ that…
This paper considers the enumeration of trees avoiding a contiguous pattern. We provide an algorithm for computing the generating function that counts n-leaf binary trees avoiding a given binary tree pattern t. Equipped with this counting…
We consider the relation between various permutation statistics and properties of permutation tableaux. We answer some of the questions of Steingrimsson and Williams (math.CO/0507149), in particular, on the distribution of the bistatistic…
We study the asymptotic number of certain monotonically labeled increasing trees arising from a generalized evolution process. The main difference between the presented model and the classical model of binary increasing trees is that the…
We consider the set of permutations that are sorted after two passes through a pop stack. We characterize these permutations in terms of forbidden patterns (classical and barred) and enumerate them according to the ascent statistic. Then we…
This paper proves that two differently defined rooted binary trees are isomorphic. The first tree is one associated to a version of Farey sequences where the vertices correspond to the open intervals formed by two successive terms in the…
We show that the Sibuya distribution and its non-critical relatives are relevant in the context of the recursive generation of both simply generated and increasing critical trees' and forests' progenies. A special class of generalized…
Asymptotic analysis on some statistical properties of the random binary-tree model is developed. We quantify a hierarchical structure of branching patterns based on the Horton-Strahler analysis. We introduce a transformation of a binary…
Permutons, which are probability measures on the unit square $[0, 1]^2$ with uniform marginals, are the natural scaling limits for sequences of (random) permutations. We introduce a $d$-dimensional generalization of these measures for all…
Random forests are an ensemble method relevant for many problems, such as regression or classification. They are popular due to their good predictive performance (compared to, e.g., decision trees) requiring only minimal tuning of…
We study the expansions of permutation statistics in the basis of functions counting occurrences of a fixed pattern in a permutation. We show the finiteness of these pattern expansions for a class of permutation statistics including the…