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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 Gaus-sian 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)
We study the consistency of listwise ranking methods with respect to the popular Normalized Discounted Cumulative Gain (NDCG) criterion. State of the art listwise approaches replace NDCG with a surrogate loss that is easier to optimize. We characterize NDCG consistency of surrogate losses to discover a surprising fact: several commonly used sur-rogates are(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)
We provide a unified framework for the high-dimensional analysis of " superposition-structured " or " dirty " statistical models: where the model parameters are a superposition of structurally constrained parameters. We allow for any number and types of structures, and any statistical model. We consider the general class of M-estimators that minimize the(More)
Undirected graphical models, such as Gaussian graphical models, Ising, and multinomial/categorical graphical models, are widely used in a variety of applications for modeling distributions over a large number of variables. These standard instances, however, are ill-suited to modeling count data, which are increasingly ubiquitous in big-data settings such as(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)
We study the general class of estimators for graphical model structure based on optimizing ℓ 1-regularized approximate log-likelihood, where the approximate likelihood uses tractable variational approximations of the partition function. We provide a message-passing algorithm that directly computes the ℓ 1 regularized approximate MLE. Further, in the case of(More)
Markov Random Fields, or undirected graph-ical models are widely used to model high-dimensional multivariate data. Classical instances of these models, such as Gaussian Graphical and Ising Models, as well as recent extensions (Yang et al., 2012) to graph-ical models specified by univariate exponential families, assume all variables arise from the same(More)
Gaussian Graphical Models (GGMs) are popular tools for studying network structures. However, many modern applications such as gene network discovery and social interactions analysis often involve high-dimensional noisy data with out-liers or heavier tails than the Gaussian distribution. In this paper, we propose the Trimmed Graphical Lasso for robust(More)