$$ \newcommand{\bigci}{\perp\mkern-10mu\perp} $$
This article is a brief overview of conditional independence in graphical models, and the related d-separation. Let us begin with a definition.
For three random variables $X$, $Y$ and $Z$, we say $X$ is conditionally independent of $Y$ given $Z$ iff
$$ p(X, Y | Z) = p(X | Z) p(Y | Z). $$
We can use a shorthand notation
$$ X \bigci Y | Z $$
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