#gaussian-prior

Question 1: Single choice

mediumAI-checkedLinear Models & Regularization

Minimizing $-\log P(\text{data} \mid \mathbf{w}) - \log P(\mathbf{w})$ finds the most probable weights a posteriori (MAP). Which prior $P(\mathbf{w})$ makes $-\log P(\mathbf{w})$ equal to the weight-decay penalty $\frac{\lambda}{2}\lVert\mathbf{w}\rVert^2$ , up to a constant?

A Gaussian centered at the least-squares weights1
A zero-mean Gaussian, $\mathbf{w} \sim \mathcal{N}(\mathbf{0}, \lambda^{-1}\mathbf{I})$ 2
A zero-mean Laplace prior, $P(\mathbf{w}) \propto \exp(-\lambda\lVert\mathbf{w}\rVert_1)$ 3
A uniform prior over all weight vectors4

Timed test