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On Semiparametric Exponential Family Graphical Models
Zhuoran Yang,Yang Ning,Han Liu +2 more
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TLDR
In this article, a new class of semiparametric exponential family graphical models for the analysis of high dimensional mixed data is proposed, and a symmetric pairwise score test for the presence of a single edge in the graph is proposed.Abstract:
We propose a new class of semiparametric exponential family graphical models for the analysis of high dimensional mixed data. Different from the existing mixed graphical models, we allow the nodewise conditional distributions to be semiparametric generalized linear models with unspecified base measure functions. Thus, one advantage of our method is that it is unnecessary to specify the type of each node and the method is more convenient to apply in practice. Under the proposed model, we consider both problems of parameter estimation and hypothesis testing in high dimensions. In particular, we propose a symmetric pairwise score test for the presence of a single edge in the graph. Compared to the existing methods for hypothesis tests, our approach takes into account of the symmetry of the parameters, such that the inferential results are invariant with respect to the different parametrizations of the same edge. Thorough numerical simulations and a real data example are provided to back up our results.read more
Citations
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Graphical Models In Applied Multivariate Statistics
TL;DR: The graphical models in applied multivariate statistics is universally compatible with any devices to read and is available in the digital library an online access to it is set as public so you can download it instantly.
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Structure Learning in Graphical Modeling
TL;DR: A graphical model is a statistical model that is associated with a graph whose nodes correspond to variables of interest as discussed by the authors, and the edges of the graph reflect allowed conditional dependencies among the variables.
ReportDOI
Valid Post-Selection and Post-Regularization Inference: An Elementary, General Approach
TL;DR: This analysis provides a set of high-level conditions under which inference for the low-dimensional parameter based on testing or point estimation methods will be regular despite selection or regularization biases occurring in the estimation of the high-dimensional nuisance parameter.
Journal ArticleDOI
Valid Post-Selection and Post-Regularization Inference: An Elementary, General Approach
TL;DR: In this article, the authors present an expository, general analysis of valid post-selection or post-regularization inference about a low-dimensional target parameter, $\alpha$, in the presence of a very high-dimensional nuisance parameter, which is estimated using modern selection or regularization methods.
ReportDOI
High-dimensional econometrics and regularized GMM
TL;DR: This chapter presents key concepts and theoretical results for analyzing estimation and inference in high-dimensional models, and presents results in a framework where estimators of parameters of interest may be represented directly as approximate means.
References
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Regression Shrinkage and Selection via the Lasso
TL;DR: A new method for estimation in linear models called the lasso, which minimizes the residual sum of squares subject to the sum of the absolute value of the coefficients being less than a constant, is proposed.
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Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties
Jianqing Fan,Runze Li +1 more
TL;DR: In this article, penalized likelihood approaches are proposed to handle variable selection problems, and it is shown that the newly proposed estimators perform as well as the oracle procedure in variable selection; namely, they work as well if the correct submodel were known.
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Decoding by linear programming
Emmanuel J. Candès,Terence Tao +1 more
TL;DR: F can be recovered exactly by solving a simple convex optimization problem (which one can recast as a linear program) and numerical experiments suggest that this recovery procedure works unreasonably well; f is recovered exactly even in situations where a significant fraction of the output is corrupted.
Book
Probabilistic graphical models : principles and techniques
Daniel L. Koller,Nir Friedman +1 more
TL;DR: The framework of probabilistic graphical models, presented in this book, provides a general approach for causal reasoning and decision making under uncertainty, allowing interpretable models to be constructed and then manipulated by reasoning algorithms.
Posted Content
Decoding by Linear Programming
Emmanuel J. Candès,Terence Tao +1 more
TL;DR: In this paper, it was shown that under suitable conditions on the coding matrix, the input vector can be recovered exactly by solving a simple convex optimization problem (which one can recast as a linear program).
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