In this paper, we describe a link between Markovian binary trees (MBT) and tree-like quasi-birth-anddeath processes (TLQBD) by associating a specific TLQBD to each MBT. The algorithms to compute the matrices Gk in the TLQBD then correspond to the algorithms calculating the extinction probability vector of the MBT. This parallelism leads to a new quadratic algorithm, based on the Newton iteratio...

The general Markov plus invariable sites (GM+I) model of biological sequence evolution is a two-class model in which an unknown proportion of sites are not allowed to change, while the remainder undergo substitutions according to a Markov process on a tree. For statistical use it is important to know if the model is identifiable; can both the tree topology and the numerical parameters be determ...

The general Markov plus invariable sites (GM + I) model of biological sequence evolution is a two-class model in which an unknown proportion of sites are not allowed to change, while the remainder undergo substitutions according to a Markov process on a tree. For statistical use it is important to know if the model is identifiable; can both the tree topology and the numerical parameters be dete...

This research was sponsored in part by U S WEST and in part by the Defense Advanced Research Projects Agency (DOD), and monitored by the Space and Naval Warfare Systems Command under Contract N0003985-C-0163, ARPA Order No. 5167. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or ...

Key points: •Trees → efficient algorithms. •Mixture → improved modeling. There are 2 approaches to improve over a single Chow-Liu tree: Bias reduction, e.g. EM algorithm [1] •Learning the mixture is viewed as a global optimization problem aiming at maximizing the data likelihood. •There is a bias-variance trade-off associated with the number of terms. • It leads to a partition of the learning s...

We propose a novel unsupervised word alignment model based on the Hidden Markov Tree (HMT) model. Our model assumes that the alignment variables have a tree structure which is isomorphic to the target dependency tree and models the distortion probability based on the source dependency tree, thereby incorporating the syntactic structure from both sides of the parallel sentences. In English-Japan...

We study the problem of projecting a distribution onto (or finding a maximum likelihood distribution among) Markov networks of bounded tree-width. By casting it as the combinatorial optimization problem of finding a maximum weight hypertree, we prove that it is NP-hard to solve exactly and provide an approximation algorithm with a provable performance guarantee.

The Markov Blanket of a target variable is the minimum conditioning set of variables that makes the target independent of all other variables. Markov Blankets inform feature selection, aid in causal discovery and serve as a basis for scalable methods of constructing Bayesian networks. This paper applies decision tree induction to the task of Markov Blanket identification. Notably, we compare (a...

We present a construction of a Lévy continuum random tree (CRT) associated with a super-critical continuous state branching process using the so-called exploration process and a Girsanov theorem. We also extend the pruning procedure to this super-critical case. Let ψ be a critical branching mechanism. We set ψθ(·) = ψ(·+ θ)− ψ(θ). Let Θ = (θ∞,+∞) or Θ = [θ∞,+∞) be the set of values of θ for whi...

In the last few years, it has become apparent that traditional wavelet-based image processing algorithms and models have significant shortcomings in their treatment of edge contours. The standard modeling paradigm exploits the fact that wavelet coefficients representing smooth regions in images tend to have small magnitude, and that the multiscale nature of the wavelet transform implies that th...