Maths for ML / Notation

\arg\min_{\theta} L(\theta)

arg min / arg max

OptimizationBeginner

Say it “the theta that minimizes L”

Not the smallest value itself, but the input that produces it.

Example

\arg\min_{x}(x-3)^2 = 3

The minimum value is 0; the arg min is 3.

In code

np.argmin(values)

torch.argmin(values)

Where you’ll see it in ML

Training = finding argmin of the loss; prediction = argmax over class scores.

Don’t confuse it with

$\min_{x} f(x),\ \max(a, b)$ min / max The smallest / largest value. With a subscript, search over that variable.
$\theta^{*}$ star The best / optimal value of something.

Lessons that use it

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