Choosing graph edges
Section of Graphical models, part of Statistical learning
Choosing graph edges
| Type | Section |
| Taught in | Graphical models |
| Part | Statistical learning |
Model selection here means choosing which edges to exclude, that is, which pairs can be treated as conditionally independent given the others. In the Gaussian model that is the search for symmetric zeros in K. Some of the better-known methods are these.
- Optimisation of an information criterion, which balances model fit against complexity: the Akaike and Bayesian information criteria.
- Stepwise optimisation by likelihood-ratio testing: compare a model with a given link against one without it. If the test supports adding or removing the link at a specified significance level, do so, and repeat until no further change is supported.
- Optimisation of predictive accuracy, which needs some balance between model fitting and model complexity.
There are 2^{p(p-1)/2} undirected simple graphs, since each unordered pair can be present or absent. Even p=10 gives about 3.5\times 10^{13} candidates. Exhaustive search quickly becomes impractical. When the sample covariance is singular, the unrestricted Gaussian precision maximum-likelihood estimate also fails to exist. A sufficiently restrictive known graph can still have a maximum-likelihood estimate, so singularity of S does not rule out every constrained fit. Regularisation provides another route, with assumptions of its own.
Used in
See also
Undirected graph · Hammersley–Clifford · A zero precision entry is conditional independence · Maximum likelihood for a known graph · Graphical lasso · Markov graphs · Graph terminology · Conditional independence