1 research outputs found
The Functional Graphical Lasso
We consider the problem of recovering conditional independence relationships
between jointly distributed Hilbertian random elements given
realizations thereof. We operate in the sparse high-dimensional regime, where
and no element is related to more than other elements. In
this context, we propose an infinite-dimensional generalization of the
graphical lasso. We prove model selection consistency under natural assumptions
and extend many classical results to infinite dimensions. In particular, we do
not require finite truncation or additional structural restrictions. The
plug-in nature of our method makes it applicable to any observational regime,
whether sparse or dense, and indifferent to serial dependence. Importantly, our
method can be understood as naturally arising from a coherent maximum
likelihood philosophy