0
$\begingroup$

We know that in probabilistic PCA, where $$x = Wz + \mu + \epsilon, \epsilon \sim N(0, I)$$ The posterior can be derived to be $$z|x \sim N\left(M^{-1}W^T(x-\mu), \sigma^{-1}M\right)$$ where $M = W^TW + \sigma^2I$. In Bishop's Pattern recognition, it said that when $\sigma^2>0$ the posterior mean shifted towards the origin relative to the orthogonal projection. Could someone help me understand this statement? When $\sigma^2 > 0$, isn't there no longer an orthogonal projection, so what is this actually comparing, what does shift toward the origin mathematically mean in this case? Thanks!

$\endgroup$

0

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Browse other questions tagged or ask your own question.