On Conditional Independence Graph Learning From Multi-Attribute Gaussian Dependent Time Series
Estimation of the conditional independence graph (CIG) of high-dimensional multivariate Gaussian time series from multi-attribute data is considered. Existing methods for graph estimation for such data are based on single-attribute models where one associates a scalar time series with each node. In multi-attribute graphical models, each node represents a random vector or vector time series. In this paper we provide a unified theoretical analysis of multi-attribute graph learning for dependent time series using a penalized log-likelihood objective function formulated in the frequency domain using the discrete Fourier transform of the time-domain data. We consider both convex (sparse-group lasso) and non-convex (log-sum and SCAD group penalties) penalty/regularization functions. We establish sufficient conditions in a high-dimensional setting for consistency (convergence of the inverse power spectral density to true value in the Frobenius norm), local convexity when using non-convex penalties, and graph recovery. We do not impose any incoherence or irrepresentability condition for our convergence results. We also empirically investigate selection of the tuning parameters based on the Bayesian information criterion, and illustrate our approach using numerical examples utilizing both synthetic and real data.
Code (0)
등록된 구현이 없습니다.
Tasks
Graph LearningSimilar Papers 제목 키워드 기반
A Copula Graphical Model for Multi-Attribute Data using Optimal Transport
Motivated by modern data forms such as images and multi-view data, the multi-attribute graphical model aims to explore the conditional independence structure among vectors. Under the Gaussian assumption, the conditional …
AttributeLearning Functional Graphs with Nonlinear Sufficient Dimension Reduction
Functional graphical models have undergone extensive development during the recent years, leading to a variety models such as the functional Gaussian graphical model, the functional copula Gaussian graphical model, the f…
On Sufficient Graphical Models
We introduce a sufficient graphical model by applying the recently developed nonlinear sufficient dimension reduction techniques to the evaluation of conditional independence. The graphical model is nonparametric in natu…
Dimensionality ReductionVariable SelectionGraph Learning from Multivariate Dependent Time Series via a Multi-Attribute Formulation
We consider the problem of inferring the conditional independence graph (CIG) of a high-dimensional stationary multivariate Gaussian time series. In a time series graph, each component of the vector series is represented…
AttributeGraph LearningTime SeriesTime Series AnalysisBinary Expansion Group Intersection Network
Conditional independence is central to modern statistics, but beyond special parametric families it rarely admits an exact covariance characterization. We introduce the binary expansion group intersection network (BEGIN)…