Maximum likelihood for a known graph
Definition taught in Graphical models, part of Statistical learning
Maximum likelihood for a known graph
| Type | Definition |
| Taught in | Graphical models |
| Part | Statistical learning |
- Initialise W=S. This presentation assumes S\succ 0.
- 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}^{*}=0 for the unconstrained edge parameters \beta^{*}. Obtain \hat\beta by padding \hat\beta^{*} with zeros in the positions of the missing edges.
- Update w_{AB}=W_{AA}\hat\beta and the corresponding row w_{BA}=w_{AB}^\top.
- In the final cycle for each j, solve for the estimated precision: \hat\theta_{AB}=-\hat\beta\,\hat\theta_{BB} with 1/\hat\theta_{BB}=s_{BB}-w_{AB}^\top\hat\beta.
Used in
- Taught in Graphical models, where the derivation and examples are.
- All 8 questions on Graphical models
See also
Undirected graph · Hammersley–Clifford · A zero precision entry is conditional independence · Graphical lasso · Markov graphs · Graph terminology · Conditional independence · Markov properties and factorisation