Consider a Gaussian stationary stochastic vector process with the property that designated pairs of components are conditionally independent given the rest of the components. Such processes can be represented on a graph where the components are nodes and the lack of a connecting link between two nodes signifies conditional independence. This leads to a sparsity pattern in the inverse of the matrix-valued spectral density. Such graphical models find applications in speech, bioinformatics, image processing, econometrics and many other fields, where the problem to fit an autoregressive (AR) model to such a process has been considered. In this paper we take this problem one step further, namely to fit an autoregressive moving-average (ARMA) model to the same data. We develop a theoretical framework and an optimization procedure which also spreads further light on previous approaches and results. This procedure is then applied to the identification problem of estimating the ARMA parameters as well as the topology of the graph from statistical data. / <p>Updated from "Preprint" to "Article" QC 20130627</p>

The Ising model is an important model in statistical physics, with over 10,000 papers published on the topic. This model assumes binary variables and only local pairwise interactions between neighbouring nodes. Inference for the general Ising model is NP-hard; this includes tasks such as calculating the partition function, finding a lowest-energy (ground) state and computing marginal probabilities. Past approaches have proceeded by working with classes of tractable Ising models, such as Ising models defined on a planar graph. For such models, the partition function and ground state can be computed exactly in polynomial time by establishing a correspondence with perfect matchings in a related graph. In this thesis we continue this line of research. In particular we simplify previous inference algorithms for the planar Ising model. The key to our construction is the complementary correspondence between graph cuts of the model graph and perfect matchings of its expanded dual. We show that our exact algorithms are effective and efficient on a number of real-world machine learning problems. We also investigate heuristic methods for approximating ground states of non-planar Ising models. We show that in this setting our approximative algorithms are superior than current state-of-the-art methods.

Thesis (M.S.)--Brigham Young University. Dept. of Mechanical Engineering, 2006. / Includes bibliographical references (p. 91-93).

Project (M.S.)--Brigham Young University. Dept. of Statistics, 2007. / Includes bibliographical references (p. 60-61).

Thesis (M.S.)--Ohio University, March, 2000. / Title from PDF t.p.

Thesis (M.S.)--Ohio University, June, 2004. / Title from PDF t.p. Includes bibliographical references (leaves 96-99).

Thesis (M.S.)--Ohio University, June, 1997. / Title from PDF t.p.

Thesis (Ph. D.)--Ohio State University, 2008. / Title from first page of PDF file. Includes bibliographical references (p. 140-150).

Thesis (Ph. D.)--University of Missouri-Columbia, 1997. / Typescript. Vita. Includes bibliographical references (leaves 280-283). Also available on the Internet.

Thesis (Ph. D.)--Auburn University, 2008. / Abstract. Includes bibliographical references (p. 119-122).