A zero precision entry is conditional independence
Theorem taught in Graphical models, part of Statistical learning
A zero precision entry is conditional independence
| Type | Theorem |
| Taught in | Graphical models |
| Part | Statistical learning |
Let X\sim\operatorname{N}_p(\mu,\Sigma) with \Sigma regular. For j\neq k,
X_j\perp X_k\mid X_{V\setminus\{j,k\}} \iff k_{jk}=0.
The zero entries of the precision matrix indicate conditional independence between the corresponding variables, with the conditioning on all the remaining variables.
Used in
- Taught in Graphical models, where the derivation and examples are.
- All 8 questions on Graphical models
See also
Precision matrix · Conditional independence · Undirected graph · Hammersley–Clifford · Maximum likelihood for a known graph · Graphical lasso · Markov graphs · Graph terminology