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Undirected graphical models, also known as Markov networks, enjoy popularity in a variety of applications. The popular instances of these models such as Gaussian Markov Random Fields (GMRFs), Ising models, and multinomial discrete models, however do not capture the characteristics of data in many settings. We introduce a new class of graphical models based(More)
Undirected graphical models, or Markov networks, are a popular class of statistical models, used in a wide variety of applications. Popular instances of this class include Gaussian graphical models and Ising models. In many settings, however, it might not be clear which subclass of graphical models to use, particularly for non-Gaussian and non-categorical(More)
UNLABELLED Hepatic resection is the most curative treatment option for early-stage hepatocellular carcinoma, but is associated with a high recurrence rate, which exceeds 50% at 5 years after surgery. Understanding the genetic basis of hepatocellular carcinoma at surgically curable stages may enable the identification of new molecular biomarkers that(More)
Markov Random Fields, or undirected graphical models are widely used to model highdimensional multivariate data. Classical instances of these models, such as Gaussian Graphical and Ising Models, as well as recent extensions (Yang et al., 2012) to graphical models specified by univariate exponential families, assume all variables arise from the same(More)
We provide a unified framework for the high-dimensional analysis of<lb>“superposition-structured” or “dirty” statistical models: where the model param-<lb>eters are a superposition of structurally constrained parameters. We allow for any<lb>number and types of structures, and any statistical model. We consider the gen-<lb>eral class of M -estimators that(More)
We consider the problem of estimating expectations of vector-valued feature functions; a special case of which includes estimating the covariance matrix of a random vector. We are interested in recovery under high-dimensional settings, where the number of features p is potentially larger than the number of samples n, and where we need to impose structural(More)
We consider the problem of structurally constrained high-dimensional linear regression. This has attracted considerable attention over the last decade, with state of the art statistical estimators based on solving regularized convex programs. While these typically non-smooth convex programs can be solved by the state of the art optimization methods in(More)