Related papers: Martingales and Profile of Binary Search Trees
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…
We develop an efficient algorithm to implement the recently introduced binary tree state (BTS) ansatz on a classical computer. BTS allows a simple approximation to permanents arising from the computationally intractable antisymmetric…
We propose a variable splitting binary tree (VSBT) model based on Bayesian context tree (BCT) models for time series segmentation. Unlike previous applications of BCT models, the tree structure in our model represents interval partitioning…
Bayesian Additive Regression Trees (BART) is a popular Bayesian non-parametric regression model that is commonly used in causal inference and beyond. Its strong predictive performance is supported by well-developed estimation theory,…
As a flexible nonparametric learning tool, the random forests algorithm has been widely applied to various real applications with appealing empirical performance, even in the presence of high-dimensional feature space. Unveiling the…
Binary search trees (BSTs) are fundamental data structures whose performance is largely governed by tree height. We introduce a block model for constructing BSTs by embedding internal BSTs into the nodes of an external BST -- a structure…
Reliable and efficient Visual Place Recognition is a major building block of modern SLAM systems. Leveraging on our prior work, in this paper we present a Hamming Distance embedding Binary Search Tree (HBST) approach for binary Descriptor…
We describe a new and computationally efficient Bayesian methodology for inferring species trees and demographics from unlinked binary markers. Likelihood calculations are carried out using diffusion models of allele frequency dynamics…
We obtain bivariate asymptotics for the number of (unicellular) combinatorial maps (a model of discrete surfaces) as both the size and the genus grow. This work is related to two research topics that have been very active recently:…
Count outcomes in longitudinal studies are frequent in clinical and engineering studies. In frequentist and Bayesian statistical analysis, methods such as Mixed linear models allow the variability or correlation within individuals to be…
We study the asymptotics of the $p$-mapping model of random mappings on $[n]$ as $n$ gets large, under a large class of asymptotic regimes for the underlying distribution $p$. We encode these random mappings in random walks which are shown…
Contextual bandits are a core technology for personalized mobile health interventions, where decision-making requires adapting to complex, non-linear user behaviors. While Thompson Sampling (TS) is a preferred strategy for these problems,…
In this thesis the properties of two kinds of non-uniform random recursive trees are studied. In the first model weights are assigned to each node, thus altering the attachment probabilities. We will call these trees weighted recursive…
We consider a model of random tree growth, where at each time unit a new vertex is added and attached to an already existing vertex chosen at random. The probability with which a vertex with degree $k$ is chosen is proportional to $w(k)$,…
This paper develops techniques to study the number of descents in random permutations via martingales. We relax an assumption in the Berry-Esseen theorem of Bolthausen (1982) to extend the theorem's scope to martingale differences of…
Adaptive binary search trees are a fundamental data structure for organizing hierarchical information. Their ability to dynamically adjust to access patterns makes them particularly valuable for building responsive and efficient networked…
In this paper, we introduce a targeted exploration strategy for the non-asymptotic, finite-time case. The proposed strategy is applicable to uncertain linear time-invariant systems subject to sub-Gaussian disturbances. As the main result,…
We study the distribution of fringe trees in Patricia tries (extending earlier results by Ischebeck (2025)) and compressed binary search trees; both cases are random binary trees that have been compressed by deleting nodes of outdegree 1 so…
A reformulation of the path length of binary search trees is given in terms of permutations, allowing to extend the definition to the instance of words, where the letters are obtained by independent geometric random variables (with…
Bayesian Additive Regression Trees (BART) is a Bayesian approach to flexible non-linear regression which has been shown to be competitive with the best modern predictive methods such as those based on bagging and boosting. BART offers some…