RI:Small:Matrix-structured statistical inference

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Many modern problems across science and engineering require the use of statistical models that describe the probabilistic relationship among the underlying variable. A core component of many of these statistical models is a matrix, comprising the parameters of the model. This proposal focuses in particular on a special subclass called graphical models that use a weighted graph to represent a distribution over the underlying variables. The main use of such statistical modeling is prediction and inference: however these tasks are typically computationally intractable or expensive for general models. An important objective is to perform these inference tasks tractably if approximately. This proposal investigates approaches that make connections with and leverage recent advances in the seemingly unrelated field of numerical linear algebra that solve linear systems in matrices by building so-called preconditioner matrices that are approximations to the linear system matrices. Such statistical and graphical models are used across science and engineering problems: indeed even our cellphones solve graphical model inference problems to decode their received signals. Speeding up these tasks is thus of tremendous importance to all of these varied applications. The researchers are involved in interdisciplinary initiatives at the University of Texas, Austin; the Institute for Computational Engineering and Sciences, and the Division of Statistics and Scientific Computation; within which they are specially involved in disseminating such cutting edge research across disciplines and courses.