Maths for ML / Notation

\int_a^b f(x)\,dx

integral

CalculusIntermediate

Say it “integral from a to b of f of x d x”

Continuous version of a sum: total area under f between a and b.

Example

\int_0^1 x\,dx = \tfrac12

In code

scipy.integrate.quad(f, a, b)

Where you’ll see it in ML

Probabilities for continuous variables, expectations, marginalizing out variables.

Don’t confuse it with

$\sum_{i=1}^{n} x_i$ summation Add up the expression for each value of the index — it's a for-loop that accumulates.
$\mathbb{E}_{x\sim p}[f(x)]$ expectation The average value you'd get if you sampled many times — weighted by probability.

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