Tag: prml

  • The equivalent kernel for non-zero prior mean

    This note is a brief addendum to Section 3.3 of Bishop on Bayesian Linear Regression. Some of the derivations in that section assume, for simplicity, that the prior mean on the weights is zero. Here we’ll relax this assumption and see what happens to the equivalent kernel. Background The setting in that section is that,…

  • Notes on the Geometry of Least Squares

    In this post I expand on the details of section 3.1.2 in Pattern Recognition and Machine Learning. We found that maximum likelihood estimation requires minimizing $$E(\mathbf w) = {1 \over 2} \sum_{n=1}^N (t_n – \ww^T \bphi(\xx_n))^2.$$ Here the vector $\bphi(\xx_n)$ contains each of our features evaluated on the single input datapoint $\xx_n$, $$\bphi(\xx_n) = [\phi_0(\xx_n),…