#affine-functions

Question 1: Single choice

easyAI-checkedLinear Models & Regularization

To get rid of the separate bias, you append a constant feature 1 to every input, $\tilde{\mathbf{x}} = (\mathbf{x}, 1)$ . Which weight vector $\tilde{\mathbf{w}}$ makes $\tilde{\mathbf{w}}^\top\tilde{\mathbf{x}} = \mathbf{w}^\top\mathbf{x} + b$ for all $\mathbf{x}$ ?

None: an affine function can't be written as a linear one1
$\tilde{\mathbf{w}} = (\mathbf{w}, b)$ 2
$\tilde{\mathbf{w}} = (\mathbf{w}, 1)$ 3
$\tilde{\mathbf{w}} = (\mathbf{w} + b\mathbf{1}, 0)$ 4

Timed test