Conditional Independence

Given mutually exclusive sets of random variables \(\mathbf{X},\mathbf{Y},\mathbf{Z}\) we say \(\mathbf{X}\) is conditionally independent of \(\mathbf{Y}\) given \(\mathbf{Z}\), denoted \(\mathbf{X} -||- \mathbf{Y}|\mathbf{Z}\) or \(\mathbb{I}_\mathbb{P}(X,Y|Z)\) if \(\mathbb{P}(\mathbf{X},\mathbf{Y}|\mathbf{Z}) = \mathbb{P}(\mathbf{X}|\mathbf{Z})\mathbb{P}(\mathbf{Y}|\mathbf{Z})\).

Conditional independence (and dependence) can be graphically represented in Bayesian Networks (BNs). Let \(X,Y,Z\) be random variables, we then have:


  • Find a way to write that independence symbol.

Author: Nazaal

Created: 2022-04-04 Mon 23:39