Confidence intervals for high-dimensional inverse covariance estimation

By Jana Jankov'a, Sara A. van de Geer. 2014

199 citations recorded by the source corpus.

We propose methodology for statistical inference for low-dimensional parameters of sparse precision matrices in a high-dimensional setting. Our method leads to a non-sparse estimator of the precision matrix whose entries have a Gaussian limiting distribution. Asymptotic properties of the novel estimator are analyzed for the case of sub-Gaussian observations under a sparsity assumption on the entries of the true precision matrix and regularity conditions. Thresholding the de-sparsified estimator gives guarantees for edge selection in the associated graphical model. Performance of the proposed method is illustrated in a simulation study.

Subfields: Statistics and Probability

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Citations in the corpus

Double/De-Biased Machine Learning of Global and Local Parameters Using Regularized Riesz Representers (2018, methodology): “To avoid such bias, we use debiased/“double” machine learning (DML) based on Neyman orthogonal scores that have zero derivative with respect to each first step learner (e.g., Neyman (1959); Belloni et al.”
Honest confidence regions and optimality in high-dimensional precision matrix estimation (2015, methodology): “Practical examples of applications of graphical modeling include modeling of brain connectivity based on FMRI brain analysis (Ng et al., 2013), genetic networks, financial data processing, social network analysis and climate data analysis. A lot of work has been done on methodology for point estimat”
A General Theory of Hypothesis Tests and Confidence Regions for Sparse High Dimensional Models (2014, methodology): “Thus, our estimator has the same asymptotic efficiency as [12, 20, 30] and is semiparametrically efficient.”
Change-point detection in high-dimensional covariance structure (2016, methodology): “For each window size n ∈ N, each central point t ∈ Tn and each side S ∈ {l, r} we define a de-sparsified estimator of precision matrix [26] [27] as”
A Projection-based Conditional Dependence Measure with Applications to High-dimensional Undirected Graphical Models. (2015, unknown): “, Fast computing for distance covariance, Technometrics, 58, 4, 435-447 (2016) [33] Jankova, J.”
Semiparametric efficiency bounds for high-dimensional models (2016, background): “…de Geer et al. (2014), Javanmard and Montanari (2014a, 2014b, 2015)], for generalized linear models [van de Geer et al. (2014)] and some special cases of nonlinear models, such as undirected graphical models [Janková and van de Geer (2014, 2017)]; we also refer here to the book van de Geer (2016).”
Structure Learning in Graphical Modeling (2016, background): “Bayesian approaches naturally include an uncertainty assessment but frequentist techniques that are able to cope with high-dimensional data are also being developed (Jankov´a & van de Geer, 2015; Ren et al., 2015; Xia et al., 2015).”
MetaboAnalyst 5.0: narrowing the gap between raw spectra and functional insights (2021, methodology): “Briefly, networks are created using a graphical LASSO model to compute the partial correlation coefficients and P-values for every pair of features in the dataset (44).”