Maths for ML / Notation

P(A \mid B)

conditional probability

Probability and statisticsBeginner

Say it “probability of A given B”

Probability of A, once you know B happened. The bar means 'given'.

Example

p(y \mid \mathbf{x};\,\theta)

A classifier: probability of label y given input x, with parameters θ.

Where you’ll see it in ML

Every predictive model is a conditional distribution; LLMs model p(next token | previous tokens).

Don’t confuse it with

$P(A),\ p(x)$ probability P(A) is the probability of event A (between 0 and 1). Lowercase p(x) is often a density or distribution.
$a \mid b$ vertical bar — many meanings Context decides: 'given' in probability, 'such that' in set-builder, 'divides' in number theory. Two bars ‖ mean a norm or KL divergence.
$\{x \mid P(x)\}$ set-builder notation Describes a set by a rule: everything before the bar, filtered by the condition after it.

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