Precision matrix
Topic of Graphical models, part of Statistical learning
Precision matrix
| Type | Topic |
| Taught in | Graphical models |
| Part | Statistical learning |
| Questions using it | 3 |
The inverse K=\Sigma^{-1} of a covariance matrix. For a multivariate normal, K_{ij}=0 exactly when variables i and j are conditionally independent given the rest, and -K_{ij}/\sqrt{K_{ii}K_{jj}} is their partial correlation.
In Graphical models
From Graphical models
Two measurements can move together because both track a third variable. To ask whether any dependence remains, one must specify what is being conditioned on. An undirected graphical model records conditional-independence restrictions through missing edges. In a nonsingular Gaussian model, these restrictions have a useful form: a missing edge corresponds to a zero off-diagonal entry of the precision matrix K=\Sigma^{-1} (Lauritzen, 1996).
Used in
- Taught in Graphical models
- Also used in Estimation and inference for the multivariate normal · Statistical classifiers and discriminant analysis · High-dimensional analysis
- Questions that use it (3) — Precision to graph · Read a Gaussian graphical model · Conditional association and sparsity
- All 8 questions on Graphical models
See also
Mean vector and covariance matrix · Multivariate normal distribution · Conditional independence · Partial correlation · A zero precision entry is conditional independence · Undirected graph · Hammersley–Clifford · Maximum likelihood for a known graph