Maths for ML / Notation

a \mid b

vertical bar — many meanings

Probability and statisticsIntermediate

Say it “given / such that / divides”

Context decides: 'given' in probability, 'such that' in set-builder, 'divides' in number theory. Two bars ‖ mean a norm or KL divergence.

Example

P(y\mid x)\ \text{vs}\ \{x \mid x>0\}

Where you’ll see it in ML

Reading p(y | x) correctly is step one for most ML papers.

Don’t confuse it with

$P(A \mid B)$ conditional probability Probability of A, once you know B happened. The bar means 'given'.
$\{x \mid P(x)\}$ set-builder notation Describes a set by a rule: everything before the bar, filtered by the condition after it.
$|x|$ absolute value Distance from zero, always non-negative. For a set, |S| is the number of elements.
$D_{\mathrm{KL}}(P \,\Vert\, Q)$ KL divergence Measures how different distribution Q is from P. Not symmetric: swapping P and Q changes the answer.

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