A1227
Title: The functional graphical lasso
Authors: Tomas Masak - Wirtschaftsuniversitaet Wien (Austria) [presenting]
Kartik Waghmare - EPFL (Switzerland)
Victor Panaretos - EPFL (Switzerland)
Abstract: The problem of recovering conditional independence relationships between $p$ jointly distributed Hilbertian random elements given $n$ realizations thereof is considered in the sparse high-dimensional regime, where $n \ll p$ and no element is related to more than $d \ll p$ other elements. An infinite-dimensional generalization of the graphical lasso is proposed in this context. Model selection consistency is proved under natural assumptions and many classical results are extended to infinite dimensions, doing away with unnecessary structural assumptions. The plug-in nature of the method makes it applicable to heterogeneous data measured under any observational regime, whether sparse or dense, and indifferent to serial dependence between samples. Moreover, the method can be understood as naturally arising from a coherent maximum likelihood philosophy.
