Maths for ML / Notation

\operatorname{Var}(X)

variance

Probability and statisticsBeginner

Say it “variance of X”

Average squared distance from the mean — how spread out a variable is.

Example

\operatorname{Var}(X) = \mathbb{E}[(X-\mu)^2]

In code

x.var()

x.var()

Where you’ll see it in ML

Init schemes (Xavier/He) are chosen to keep activation variance stable.

Don’t confuse it with

$\sigma,\ \sigma^2,\ \sigma(z)$ sigma Lowercase σ is the standard deviation (σ² the variance) — or, as a function σ(z), the sigmoid. Capital Σ is a sum or a covariance matrix.
$\boldsymbol{\Sigma} = \operatorname{Cov}(\mathbf{x})$ covariance matrix Matrix whose entries say how pairs of features vary together. Same symbol as sum — context (bold, no limits) tells you which.

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