Maths for ML / Notation

\prod_{i=1}^{n} x_i

product

Sums and productsBeginner

Say it “product from i equals 1 to n of x i”

Multiply the expression together for every value of the index.

Example

\prod_{i=1}^{3} i = 6

In code

np.prod(x)

torch.prod(x)

Where you’ll see it in ML

Likelihood of i.i.d. data is a product of probabilities — which is why we take logs to turn it into a sum.

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.
$\pi$ pi About 3.14159 — the circle constant. In RL, π is a policy instead.
$\log x,\ \ln x$ logarithm The inverse of exp: what power of the base gives x. In ML papers log almost always means natural log (base e).

Lessons that use it

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