Related papers: Binarization Trees and Random Number Generation
The use of machine learning algorithms in finance, medicine, and criminal justice can deeply impact human lives. As a consequence, research into interpretable machine learning has rapidly grown in an attempt to better control and fix…
This paper introduces a new combinatorial framework for modeling the growth of binary trees through a discrete evolution process that incorporates a growing rule and an extinction rule. Building upon the theory of increasingly labeled…
Topologically constrained genome-like polymers often double-fold into tree-like configurations, which can be modelled on the level of folded (ring) polymers or on the level of the underlying random trees. For both descriptions, we have…
Measuring the complexity of tree structures can be beneficial in areas that use tree data structures for storage, communication, and processing purposes. This complexity can then be used to compress tree data structures to their…
We study the extreme local structure of plane binary trees through the distribution of leaves at maximum depth. We first address two basic questions: (i) the asymptotic probability that exactly two leaves occur at the deepest level, and…
We consider random binary trees that appear as the output of certain standard algorithms for sorting and searching if the input is random. We introduce the subtree size metric on search trees and show that the resulting metric spaces…
Multiple binomial sums form a large class of multi-indexed sequences, closed under partial summation, which contains most of the sequences obtained by multiple summation of products of binomial coefficients and also all the sequences with…
Due to their long-standing reputation as excellent off-the-shelf predictors, random forests continue remain a go-to model of choice for applied statisticians and data scientists. Despite their widespread use, however, until recently, little…
We consider the problem of lossless compression of binary trees, with the aim of reducing the number of code bits needed to store or transmit such trees. A lossless grammar-based code is presented which encodes each binary tree into a…
Hierarchical structure is ubiquitous in data across many domains. There are many hierarchical clustering methods, frequently used by domain experts, which strive to discover this structure. However, most of these methods limit discoverable…
A tanglegram consists of two binary rooted trees with the same number of leaves and a perfect matching between the leaves of the trees. We show that the two halves of a random tanglegram essentially look like two independently chosen random…
Classification and Regression Trees (CARTs) are off-the-shelf techniques in modern Statistics and Machine Learning. CARTs are traditionally built by means of a greedy procedure, sequentially deciding the splitting predictor variable(s) and…
Probability estimation is one of the fundamental tasks in statistics and machine learning. However, standard methods for probability estimation on discrete objects do not handle object structure in a satisfactory manner. In this paper, we…
Binarization is a powerful compression technique for neural networks, significantly reducing FLOPs, but often results in a significant drop in model performance. To address this issue, partial binarization techniques have been developed,…
We present a new uniform random sampler for binary trees with $n$ internal nodes consuming $2n + \Theta(\log(n)^2)$ random bits on average. This makes it quasi-optimal and out-performs the classical Remy algorithm. We also present a sampler…
A function on an algebra is congruence preserving if, for any congruence, it maps pairs of congruent elements onto pairs of congruent elements. We show that on the algebra of binary trees whose leaves are labeled by letters of an alphabet…
A binary tanglegram is a pair <S,T> of binary trees whose leaf sets are in one-to-one correspondence; matching leaves are connected by inter-tree edges. For applications, for example in phylogenetics or software engineering, it is required…
We present a simple trimming algorithm that generates nested uniform binary plane trees by removing leaves one-by-one using a best-of-three-match procedure. While its one-step transition specializes to the Luczak-Winkler & Caraceni-Stauffer…
Alphabetic codes and binary search trees are combinatorial structures that abstract search procedures in ordered sets endowed with probability distributions. In this paper, we design new linear-time algorithms to construct alphabetic codes,…
We obtain new non-asymptotic tail bounds for the height of uniformly random trees with a given degree sequence, simply generated trees and conditioned Bienaym\'e trees (the family trees of branching processes), in the process settling three…