Ridge regression from scratch

Implement ridge regression and the polynomial features to try it on.

• poly_features(x, degree): for a 1-D array x, return an array of shape (len(x), degree) with columns $x,x^2,\dots ,x^{\text{degree}}$ (no constant column).
• ridge_fit(X, y, lam): return (w, b) minimising $\frac{1}{n}\Vert X\mathbf{w}+b-\mathbf{y}{\Vert }^2+\lambda \Vert \mathbf{w}{\Vert }^2$, without penalising b. Trick: centre X and y (subtract their means), solve $(X_c^{\top }{X}_c+n\lambda I)\mathbf{w}=X_c^{\top }{y}_c$, then b = y.mean() - X.mean(axis=0) @ w.