Lesson 6.4ModelCode~55 min

Classification

Yes-or-no predictions with the sigmoid, and the decision boundary it draws.

Module 6 · 0/11 done

Yes-or-no questions

Many problems aren’t “how much?” but “which one?”. Spam or not. Pass or fail. Tumour or not. This is classification, and a straight line alone is the wrong tool: a line outputs any number, but we want a probability between 0 and 1.

The fix: compute the line as before, then squash its output with the sigmoid function, $\sigma$ :

\violet{p} = \sigma(\green{w}\blue{x} + \green{b})

\sigma(z) = \frac{1}{1 + e^{-z}}

Try itThe S-curve

const sigmoid = (z: number) => 1 / (1 + Math.exp(-z))
plot.fn(sigmoid, [-8, 8], { title: "σ(z) squashes any number into (0, 1)" })
console.log(sigmoid(-100), sigmoid(0), sigmoid(100))

Press Run (⌘/Ctrl + Enter) to see output here.

Huge negative inputs give almost 0, huge positive ones almost 1, and 0 gives exactly 0.5. Perfect for a probability.