Partial correlation graphical LASSO
Standard likelihood penalties to learn Gaussian graphical models are based on regularizing the off-diagonal entries of the precision matrix. Such methods, and their Bayesian counterparts, are not invariant to scalar multiplication of the variables, unless one standardizes the observed data to unit s...
| Authors: | , , |
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| Format: | article |
| Status: | Published version |
| Publication Date: | 2023 |
| Country: | España |
| Institution: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repository: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:10230/70162 |
| Online Access: | http://hdl.handle.net/10230/70162 http://dx.doi.org/10.1111/sjos.12675 |
| Access Level: | Open access |
| Keyword: | Covariance matrix estimation Gaussian graphical model Gaphical LASSO Partial correlation Penalized likelihood Precision matrix |
| Summary: | Standard likelihood penalties to learn Gaussian graphical models are based on regularizing the off-diagonal entries of the precision matrix. Such methods, and their Bayesian counterparts, are not invariant to scalar multiplication of the variables, unless one standardizes the observed data to unit sample variances. We show that such standardization can have a strong effect on inference and introduce a new family of penalties based on partial correlations. We show that the latter, as well as the maximum likelihood, L0 and logarithmic penalties are scale invariant. We illustrate the use of one such penalty, the partial correlation graphical LASSO, which sets an L1 penalty on partial correlations. The associated optimization problem is no longer convex, but is conditionally convex. We show via simulated examples and in two real datasets that, besides being scale invariant, there can be important gains in terms of inference. |
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