A central task in the study of molecular sequence data from present-day species is the reconstruction of the ancestral relationships. The most established approach to tree reconstruction is the maximum likelihood (ML) method. In this method, evolution is described in terms of a discrete-state continuous-time Markov process on a phylogenetic tree. The substitution rate matrix, that determines th...

Prediction by Partial Match (PPM) is a commonly used technique in Web prefetching, where prefetching decisions are made based on historical URLs in a dynamically maintained Markov prediction tree. Existing approaches either widely store the URL nodes by building the tree with a fixed height in each branch, or only store the branches with frequently accessed URLs. Building the popularity informa...

Abstract: Decomposable graphs are known for their tedious and complicated Markov update steps. Instead of modelling them directly, this work introduces a class of tree-dependent bipartite graphs that span the projective space of decomposable graphs. This is achieved through dimensionality expansion that causes the graph nodes to be conditionally independent given a latent tree. The Markov updat...

One of the major tasks of evolutionary biology is the reconstruction of phylogenetic trees from molecular data. The evolutionary model is given by a Markov chain on the true evolutionary tree. Given samples from this Markov chain at the leaves of the tree, the goal is to reconstruct the evolutionary tree. It is well known that in order to reconstruct a tree on n leaves, sequences of length Ω(lo...

This paper discusses hidden Markov model-based context-dependent phoneme modelling and their associated problems, particulary data insufficiency and unseen triphones. The implementation of decision tree-based state clustering, a technique suitable for solving these problems, is discussed. This technique was first proposed in 1994 by Young, Woodland and Odell [1]. A triphone-based phoneme recogn...

Abstract. In this paper we obtain exponential upper bounds for the rate of convergence of a version of the algorithm Context, when the underlying tree is not necessarily bounded. The algorithm Context is a well-known tool to estimate the context tree of a Variable Length Markov Chain. As a consequence of the exponential bounds we obtain a strong consistency result. We generalize in this way sev...

We describe a new algorithm, Relaxed Survey Propagation (RSP), for finding MAP configurations in Markov random fields. We compare its performance with state-of-the-art algorithms including the max-product belief propagation, its sequential tree-reweighted variant, residual (sum-product) belief propagation, and tree-structured expectation propagation. We show that it outperforms all approaches f...

We give a new, simple construction of the α-stable tree for α ∈ (1, 2]. We obtain it as the closure of an increasing sequence of R-trees inductively built by gluing together line-segments one by one. The lengths of these line-segments are related to the the increments of an increasing R+-valued Markov chain. For α = 2, we recover Aldous’ line-breaking construction of the Brownian continuum rand...

The paper introduces an input-driven generative model for tree-structured data that extends the bottom-up hidden tree Markov model with non-homogenous transition and emission probabilities. The advantage of introducing an input-driven dynamics in structured-data processing is experimentally investigated. The results of this preliminary analysis suggest that input-driven models can capture more ...

Given a group-based Markov model on a tree, one can compute the vertex representation of a polytope which describes the associated toric variety. The half-space representation, however, is not easily computable. In the case of Z2 or Z2 × Z2, these polytopes have applications in the field of phylogenetics. We provide a half-space representation for the m-claw tree where G = Z2 × Z2, which corres...