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Quantifying Nonlocal Informativeness in HighDimensional, Loopy Gaussian Graphical Models
"... We consider the problem of selecting informative observations in Gaussian graphical models containing both cycles and nuisances. More specifically, we consider the subproblem of quantifying conditional mutual information measures that are nonlocal on such graphs. The ability to efficiently quant ..."
Abstract

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We consider the problem of selecting informative observations in Gaussian graphical models containing both cycles and nuisances. More specifically, we consider the subproblem of quantifying conditional mutual information measures that are nonlocal on such graphs. The ability to efficiently quantify the information content of observations is crucial for resourceconstrained data acquisition (adaptive sampling) and data processing (active learning) systems. While closedform expressions for Gaussian mutual information exist, standard linear algebraic techniques, with complexity cubic in the network size, are intractable for highdimensional distributions. We investigate the use of embedded trees for computing nonlocal pairwise mutual information and demonstrate through numerical simulations that the presented approach achieves a significant reduction in computational cost over inversionbased methods. 1
Focused Active Inference
, 2014
"... In resourceconstrained inferential settings, uncertainty can be efficiently minimized with respect to a resource budget by incorporating the most informative subset of observations – a problem known as active inference. Yet despite the myriad recent advances in both understanding and streamlining ..."
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In resourceconstrained inferential settings, uncertainty can be efficiently minimized with respect to a resource budget by incorporating the most informative subset of observations – a problem known as active inference. Yet despite the myriad recent advances in both understanding and streamlining inference through probabilistic graphical models, which represent the structural sparsity of distributions, the propagation of information measures in these graphs is less well understood. Furthermore, active inference is an NPhard problem, thus motivating investigation of bounds on the suboptimality of heuristic observation selectors. Prior work in active inference has considered only the unfocused problem, which assumes all latent states are of inferential interest. Often one learns a sparse, high