Related papers: Average Size of a Suffix Tree for Markov Sources
The goal of these lectures is to survey some of the recent progress on the description of large-scale structure of random trees. We use the framework of Markov-Branching sequences of trees and discuss several applications.
We study phylogenetic signal present in syntactic information by considering the syntactic structures data from Longobardi (2017b), Collins (2010), Ceolin et al. (2020) and Koopman (2011). Focusing first on the general Markov models, we…
A Markov tree is a random vector indexed by the nodes of a tree whose distribution is determined by the distributions of pairs of neighbouring variables and a list of conditional independence relations. Upon an assumption on the tails of…
The classes of tree permutations and forest permutations were defined by Acan and Hitczenko (2016). We study random permutations of a given length from these classes, and in particular the number of occurrences of a fixed pattern in one of…
In this paper we review some recent results that shed light on a fundamental question in molecular systematics: how much phylogenetic `signal' can we expect from characters that have evolved under some Markov process? There are many sides…
In this paper we investigate the use of staged tree models for discrete longitudinal data. Staged trees are a type of probabilistic graphical model for finite sample space processes. They are a natural fit for longitudinal data because a…
This paper proposed an approach to automatically discovering subject dimension, action dimension, object dimension and adverbial dimension from texts to efficiently operate texts and support query in natural language. The high quality of…
Understanding the effects of the choice of the tree on the joint distribution of a tree-structured Markov random field (MRF) is crucial for fully exploiting the intelligibility of such probabilistic graphical models. Tools must be developed…
Motivated by the evident success of context-tree based methods in lossless data compression, we explore, in this paper, methods of the same spirit in universal prediction of individual sequences. By context-tree prediction, we refer to a…
We introduce block Markov chains (BMCs) indexed by an infinite rooted tree. It turns out that BMCs define a new class of tree-indexed Markovian processes. We clarify the structure of BMCs in connection with Markov chains (MCs) and Markov…
A consensus tree is a phylogenetic tree that synthesizes a given collection of phylogenetic trees, all of which share the same leaf labels but may have different topologies, typically obtained through bootstrapping. Our research focuses on…
Geometry of networks endowed with a causal structure is discussed using the conventional framework of equilibrium statistical mechanics. The popular growing network models appear as particular causal models. We focus on a class of tree…
We propose a procedure to build a decision tree which approximates the performance of complex machine learning models. This single approximation tree can be used to interpret and simplify the predicting pattern of random forests (RFs) and…
Infinite random sequences of letters can be viewed as stochastic chains or as strings produced by a source, in the sense of information theory. The relationship between Variable Length Markov Chains (VLMC) and probabilistic dynamical…
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…
Dependency trees have proven to be a very successful model to represent the syntactic structure of sentences of human languages. In these structures, vertices are words and edges connect syntactically-dependent words. The tendency of these…
We prime-encode the natural numbers via recursive factorisation, iterated to the exponents, generating a corpus of planar rooted trees equivalently represented as Dyck words. This forms a deterministic text endowed with internal rules.…
We investigate the rank of the average mixing matrix of trees, with all eigenvalues distinct. The rank of the average mixing matrix of a tree on $n$ vertices with $n$ distinct eigenvalues is upper-bounded by $\frac{n}{2}$. Computations on…
We estimate the size of a labelled tree by comparing the amount of (labelled) nodes with the size of the set of labels. Roughly speaking, a exponentially big labelled tree, is any labelled tree that has an exponential gap between its size,…
Although regular expressions do not correspond univocally to regular languages, it is still worthwhile to study their properties and algorithms. For the average case analysis one often relies on the uniform random generation using a…