In recent years, there has been a growing interest in problems in graph estimation and model selection, which all share very similar matrix variational formulations, the most popular one being probably GLASSO. Unfortunately, the standard GLASSO formulation does not take into account noise corrupting the data: this shortcoming leads us to propose a novel criterion, where the regularization function is decoupled in two terms, one acting only on the eigenvalues of the matrix and the other on the matrix elements. Incorporating noise information into the model has the side-effect to make the cost function non-convex. To overcome this difficulty, we adopt a majorization-minimization approach, where at each iteration a convex approximation of the original cost function is minimized via the Douglas-Rachford procedure. The achieved results are very promising w.r.t. classical approaches.

A nonconvex variational approach for robust graphical lasso / A. Benfenati, E. Chouzenoux, J.-. Pesquet (PROCEEDINGS OF THE ... IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH, AND SIGNAL PROCESSING). - In: 2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)[s.l] : IEEE, 2018. - ISBN 9781538646588. - pp. 3969-3973 (( convegno IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) tenutosi a Calgary nel 2018 [10.1109/ICASSP.2018.8462421].

A nonconvex variational approach for robust graphical lasso

A. Benfenati
;
2018

Abstract

In recent years, there has been a growing interest in problems in graph estimation and model selection, which all share very similar matrix variational formulations, the most popular one being probably GLASSO. Unfortunately, the standard GLASSO formulation does not take into account noise corrupting the data: this shortcoming leads us to propose a novel criterion, where the regularization function is decoupled in two terms, one acting only on the eigenvalues of the matrix and the other on the matrix elements. Incorporating noise information into the model has the side-effect to make the cost function non-convex. To overcome this difficulty, we adopt a majorization-minimization approach, where at each iteration a convex approximation of the original cost function is minimized via the Douglas-Rachford procedure. The achieved results are very promising w.r.t. classical approaches.
Majorization-minimization; Graphical LASSO; Non-convex Optimization; Covariance Estimation; Proximal Methods
Settore MAT/08 - Analisi Numerica
The Institute of Electrical and Electronics Engineers Signal Processing Society
Book Part (author)
File in questo prodotto:
File Dimensione Formato  
08462421.pdf

accesso riservato

Tipologia: Publisher's version/PDF
Dimensione 357.3 kB
Formato Adobe PDF
357.3 kB Adobe PDF   Visualizza/Apri   Richiedi una copia
ICASSP.pdf

accesso aperto

Tipologia: Pre-print (manoscritto inviato all'editore)
Dimensione 319.31 kB
Formato Adobe PDF
319.31 kB Adobe PDF Visualizza/Apri
Pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/652721
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 3
  • ???jsp.display-item.citation.isi??? 3
social impact