Rasmussen and Williams (5.1) give the following notation for the SE-ARD kernel:

$\begin{aligned}k(\mathbf{x}_p,\mathbf{x}_q)&=\sigma^2_f\hspace{0.5em} exp \left( -\frac{1}{2} (\mathbf{x}_p - \mathbf{x}_q)^\top M(\mathbf{x}_p - \mathbf{x}_q) \right)+\sigma^2_n \delta_{pq}\\ M&=\text{diag}(l)^{-2}, \hspace{1em} l \hspace{0.5em} \text{a positive vector}\end{aligned}$

They cite Neal's 1996 thesis, which in (4.3.1) conjectures about "informative priors for the hyperparameters associated with the inputs".

I'm searching for references implementing these "priors over hyperparameters":

  1. What are some good implementations of $l$ is a mixture?
  2. A spike/slab mixture would be consistent with the original goal of ARD, but I'm most interested in approaches where the goal is clustering over the $l_i$'s
  3. More general references are better, but my immediate application would utilize a logistic or probit link for binary classification.

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