Graphical lasso
Definition taught in Graphical models, part of Statistical learning
Graphical lasso
| Type | Definition |
| Taught in | Graphical models |
| Part | Statistical learning |
| Questions using it | 2 |
- Initialise W=S+\lambda I.
- Repeat for j=1,\ldots,p until convergence:
- Partition W into part A, all but the jth row and column, and part B, the jth row and column.
- Solve W_{AA}\beta-s_{AB}+\lambda z=0, where z_k=\operatorname{sign}(\beta_k) for \beta_k\neq 0 and z_k\in[-1,1] for \beta_k=0, using cyclic coordinate descent.
- Update w_{AB}=W_{AA}\hat\beta and the corresponding row w_{BA}=w_{AB}^\top.
- In the final cycle for each j, solve \hat\theta_{AB}=-\hat\beta\,\hat\theta_{BB} with 1/\hat\theta_{BB}=w_{BB}-w_{AB}^\top\hat\beta.
Used in
- Taught in Graphical models, where the derivation and examples are.
- Questions that use it (2) — A tempting wrong turn (answer) · Conditional association and sparsity
- All 8 questions on Graphical models
See also
Sparsity · Undirected graph · Hammersley–Clifford · A zero precision entry is conditional independence · Maximum likelihood for a known graph · Markov graphs · Graph terminology · Conditional independence