
Model Uncertainty and Correctability for Directed Graphical Models
Probabilistic graphical models are a fundamental tool in probabilistic m...
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Learning Loosely Connected Markov Random Fields
We consider the structure learning problem for graphical models that we ...
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Lagrangian uncertainty quantification and information inequalities for stochastic flows
We develop a systematic informationtheoretic framework for quantificati...
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Gaussian Experts Selection using Graphical Models
Local approximations are popular methods to scale Gaussian processes (GP...
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HingeLoss Markov Random Fields and Probabilistic Soft Logic
A fundamental challenge in developing highimpact machine learning techn...
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A Quotient Space Formulation for Statistical Analysis of Graphical Data
Complex analyses involving multiple, dependent random quantities often l...
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Neural density estimation and uncertainty quantification for laser induced breakdown spectroscopy spectra
Constructing probability densities for inference in highdimensional spe...
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Uncertainty quantification for Markov Random Fields
We present an informationbased uncertainty quantification method for general Markov Random Fields. Markov Random Fields (MRF) are structured, probabilistic graphical models over undirected graphs, and provide a fundamental unifying modeling tool for statistical mechanics, probabilistic machine learning, and artificial intelligence. Typically MRFs are complex and highdimensional with nodes and edges (connections) built in a modular fashion from simpler, lowdimensional probabilistic models and their local connections; in turn, this modularity allows to incorporate available data to MRFs and efficiently simulate them by leveraging their graphtheoretic structure. Learning graphical models from data and/or constructing them from physical modeling and constraints necessarily involves uncertainties inherited from data, modeling choices, or numerical approximations. These uncertainties in the MRF can be manifested either in the graph structure or the probability distribution functions, and necessarily will propagate in predictions for quantities of interest. Here we quantify such uncertainties using tight, information based bounds on the predictions of quantities of interest; these bounds take advantage of the graphical structure of MRFs and are capable of handling the inherent highdimensionality of such graphical models. We demonstrate our methods in MRFs for medical diagnostics and statistical mechanics models. In the latter, we develop uncertainty quantification bounds for finite size effects and phase diagrams, which constitute two of the typical predictions goals of statistical mechanics modeling.
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