This paper describes a probabilistic algorithm that, given a connected, undirected graph G with n vertices, produces a spanning tree of G chosen uniformly at random among the spanning trees of G. The expected running time is O(n logn) per generated tree for almost all graphs, and O(n3) for the worst graphs. Previously known deterministic algorithms and much more complicated and require O(n3) ti...

By introducing the asymptotic logarithmic likelihood ratio as a measure of the Markov approximation of arbitrary random fields on a uniformly bounded tree, by constructing a non-negative martingale on a uniformly bounded tree, a class of small deviation theorems of functionals and a class of small deviation theorems of the frequencies of occurrence of states for random fields on a uniformly bou...

A widely-studied model for generating binary sequences is to ‘evolve’ them on a tree according to a symmetric Markov process. We show that under this model distinguishing the true (model) tree from a false one is substantially “easier” (in terms of the sequence length needed) than determining the true tree. The key tool is a new and tight Ramsey-type result for binary trees.

We present a method for summarising collections of phylogenetic trees that extends the notion of consensus trees. Each branch in a phylogenetic tree corresponds to a bipartition or split of the set of taxa labelling its leaves. Given a collection of phylogenetic trees, each labelled by the same set of taxa, all those splits that appear in more than a predefined threshold proportion of the trees...

In evaluating the performance of online algorithms for search trees, one wants to compare them to the best offline algorithm available. In this paper we lower bound the cost of an optimal offline binary search tree using the Kolmogorov complexity of the request sequence. We obtain several applications for this result. First, any offline binary search tree algorithm can be at most a constant fac...

The problem of predicting user’s behavior on a Web site has fundamental significance due to the rapid growth of the World Wide Web. Although traditional Markov models have been found to be suited for addressing this problem, they have serious limitations. Thus, good predictions require new Markov models. Hybrid-order tree-like Markov models predict Web access precisely while providing high cove...

The variations between homologous nucleotide sequences representative of various species are, in part, a consequence of the evolutionary history of these species. Determining the evolutionary tree from patterns in the sequences depends on inverting the stochastic processes governing the substitutions from their ancestral sequence. We present a nl.J.mber of recent (and some new) results which al...

In large-vocabulary speech recognition, we often encounter triphones that are not covered in the training data. These unseen triphones are usually backed off to their corresponding diphones or context-independent phones, which contain less context yet have plenty of training examples. In this paper, we propose to use decision-tree-based senones to generate needed senonic baseforms for these uns...

Increasing web content and Internet traffic is making web prediction models popular. A web prediction model helps to predict user requests ahead of time, making web servers more responsive. It caches these pages at the server side or pre-sends the response to the client to reduce web latency. Several prediction techniques have been tried in the past; Markov based prediction models being the mos...

This work considers the problem of learning the structure of multivariate linear tree models, whichinclude a variety of directed tree graphical models with continuous, discrete, and mixed latent variablessuch as linear-Gaussian models, hidden Markov models, Gaussian mixture models, and Markov evolu-tionary trees. The setting is one where we only have samples from certain observe...