Related papers: Average Size of a Suffix Tree for Markov Sources

Phylogenetics uses alignments of molecular sequence data to learn about evolutionary trees relating species. Along branches, sequence evolution is modelled using a continuous-time Markov process characterised by an instantaneous rate…

Strong typicality and the Markov lemma have been used in the proofs of several multiterminal source coding theorems. Since these two tools can be applied to finite alphabets only, the results proved by them are subject to the same…

The suffix trees are fundamental data structures for various kinds of string processing. The suffix tree of a text string $T$ of length $n$ has $O(n)$ nodes and edges, and the string label of each edge is encoded by a pair of positions in…

We study the problem of how well a tree metric is able to preserve the sum of pairwise distances of an arbitrary metric. This problem is closely related to low-stretch metric embeddings and is interesting by its own flavor from the line of…

Neural networks with tree-based sentence encoders have shown better results on many downstream tasks. Most of existing tree-based encoders adopt syntactic parsing trees as the explicit structure prior. To study the effectiveness of…

We assess advantages of expressing tree-structured Ising models via their mean parameterization rather than their commonly chosen canonical parameterization. This includes fixedness of marginal distributions, often convenient for dependence…

An inequality of K. Marton shows that the joint distribution of a Markov chain with uniformly contracting transition kernels exhibits concentration. We prove an analogous inequality for broadcast models on finite trees. We use this…

The task of calculating similarities between strings held by different organizations without revealing these strings is an increasingly important problem in areas such as health informatics, national censuses, genomics, and fraud detection.…

Given a gene tree and a species tree, ancestral configurations represent the combinatorially distinct sets of gene lineages that can reach a given node of the species tree. They have been introduced as a data structure for use in the…

We consider combinatorial aspects of $\lambda$-terms in the model based on de Bruijn indices where each building constructor is of size one. Surprisingly, the counting sequence for $\lambda$-terms corresponds also to two families of binary…

In this paper, we propose a new indexing structure for parameterized strings which we call PLSTs, by generalizing linear-size suffix tries for ordinary strings. Two parameterized strings are said to match if there is a bijection on the…

We consider uniform random permutations drawn from a family enumerated through generating trees. We develop a new general technique to establish a central limit theorem for the number of consecutive occurrences of a fixed pattern in such…

A new synthesis scheme is proposed to effectively generate a random vector with prescribed joint density that induces a (latent) Gaussian tree structure. The quality of synthesis is measured by total variation distance between the…

Suffix trees have emerged to be very fast for pattern searching yielding O (m) time, where m is the pattern size. Unfortunately their high memory requirements make it impractical to work with huge amounts of data. We present a memory…

This paper studies a Markov chain for phylogenetic reconstruction which uses a popular transition between tree topologies known as subtree pruning-and-regrafting (SPR). We analyze the Markov chain in the simpler setting that the generating…

The seminal work of Chow and Liu (1968) shows that approximation of a finite probabilistic system by Markov trees can achieve the minimum information loss with the topology of a maximum spanning tree. Our current paper generalizes the…

Real world systems typically feature a variety of different dependency types and topologies that complicate model selection for probabilistic graphical models. We introduce the ensemble-of-forests model, a generalization of the…

We address the issue of context tree estimation in variable length hidden Markov models. We propose an estimator of the context tree of the hidden Markov process which needs no prior upper bound on the depth of the context tree. We prove…

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…

This paper describes a method for creating structure from heterogeneous sources, as part of an information database, or more specifically, a 'concept base'. Structures called 'concept trees' can grow from the semi-structured sources when…