English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper, we introduce a new directed graphical model from Gaussiandata: the Gaussian graphical interaction model (GGIM). The development of thismodel comes from considering stationary Gaussian processes on graphs, andleveraging the equations between the resulting steady-state covariance matrixand the Laplacian matrix representing the interaction graph. Through thepresentation of conceptually straightforward theory, we develop the new modeland provide interpretations of the edges in the graphical model in terms ofstatistical measures. We show that when restricted to undirected graphs, theLaplacian matrix representing a GGIM is equivalent to the standard inversecovariance matrix that encodes conditional dependence relationships.Furthermore, our approach leads to a natural definition of directed conditionalindependence of two elements in a stationary Gaussian process. We demonstratethat the problem of learning sparse GGIMs for a given observation set can beframed as a LASSO problem. By comparison with the problem of inverse covarianceestimation, we prove a bound on the difference between the covariance matrixcorresponding to a sparse GGIM and the covariance matrix corresponding to the$l_1$-norm penalized maximum log-likelihood estimate. Finally, we consider theproblem of learning GGIMs associated with sparse directed conditionaldependence relationships. In all, the new model presents a novel perspective ondirected relationships between variables and significantly expands on the stateof the art in Gaussian graphical modeling.

Learning Directed Graphical Models from Gaussian Data