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Continuously indexed graphical models
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DOI：10.1093/jrsssb/qkae086.png)
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Abstract
En 中文
Let X={Xu}u is an element of U be a real-valued Gaussian process indexed by a set U. We show that X can be viewed as a graphical model with an uncountably infinite graph, where each Xu is a vertex. This graph is characterized by the reproducing property of X's covariance kernel, without restricting U to be finite or countable, allowing the modelling of stochastic processes in continuous time/space. Unlike traditional methods, this characterization is not based on zero entries of an inverse covariance, posing challenges for structure estimation. We propose a plug-in methodology that targets graph recovery up to a finite resolution and shows consistency for graphs which are sufficiently regular and that can be applied to virtually any measurement regime. Furthermore, we derive convergence rates and finite-sample guarantees for the method, and demonstrate its performance through a simulation study and two data analyses.
Keywords:
graphical models
Gaussian processes
reproducing kernels
conditional independence
Journal
J
IF:
3.6
Papers:
1.5K
Citations:
3.2W