Given a Gaussian Markov random field, we consider the problem of selecting a subset of variables to observe which minimizes the total expected squared prediction error of the unobserved variables. We first show that finding an exact solution is NP-hard even for a restricted class of Gaussian Markov random fields, called Gaussian free fields, which arise in semi-supervised learning and computer ...

In this paper, we discuss how to check Probablistic Computation Tree Logic (PCTL) logic operators over infinite state Discrete Time Markov Chains (DTMC). Probabilistic model checking has been largely applied over finite state space Markov models. Recently infinite state models have been considered when underlying infinite Markov models have special structures. We propose to consider finite stat...

Feedback signaling plays a crucial role in flow control because the traffic source relies on the signaling information to make correct and timely flow-control decisions. However, it is difficult to design an efficient signaling algorithm since each signaling message can tolerate neither error nor latency. Multicast flow-control signaling imposes two additional challenges: scalability and feedba...

In this paper we use the Bayesian network as a tool of explorative analysis: its theory guarantees that, given the structure and some assumptions, the Markov blanket of a variable is the minimal conditioning set through which the variable is independent from all the others. We use the Markov blanket of a target variable to extract the relevant features for constructing a decision tree (DT). Our...

In this article we present an alternative method for defining the question set used for the induction of acoustic phonetic decision trees. The method is data driven and employs local similarities between the probability density functions of hidden Markov models. The method is shown to work at least as well as the standard method using question sets devised by human experts.

Many of the stochastic models used in inference of phylogenetic trees from biological sequence data have polynomial parameterization maps. The image of such a map—the collection of joint distributions for all parameter choices—forms the model space. Since the parameterization is polynomial, the Zariski closure of the model space is an algebraic variety which is typically much larger than the mo...

In this paper we describe our approach to tracing the evolution of several piggyBAC transposons, starting from a phylogenetic tree through building a Hidden Markov Model, finally arriving with a group of potentially related sequences that shows the conservation of this group of piggyBAC transposons across a wide range of organisms.

This monograph presents some new concentration inequalities for Feynman-Kac particle processes. We analyze different types of stochastic particle models, including particle profile occupation measures, genealogical tree based evolution models, particle free energies, as well as backward Markov chain particle models. We illustrate these results with a series of topics related to computational ph...

Semi-global matching, originally introduced in the context of dense stereo, is a very successful heuristic to minimize the energy of a pairwise multi-label Markov Random Field defined on a grid. We offer the first principled explanation of this empirically successful algorithm, and clarify its exact relation to belief propagation and tree-reweighted message passing. One outcome of this new conn...

We study consistent collections of random fragmentation trees with random integervalued edge lengths. We prove several equivalent necessary and sufficient conditions under which Geometrically distributed edge lengths can be consistently assigned to a Markov branching tree. Among these conditions is a characterization by a unique probability measure, which plays a role similar to the dislocation...