+1 for using GPs for hyperparameter search algorithms and for adding
gradient-based optimization.

I would like to add that it would be nice to have less redundancy
between the GP's correlation_models and the kernels in pairwise.
Additionally, it would be nice if kernels could be specified externally
to sklearn and passed as callables to the GP in a similar way as it is
implemented in the other kernel-methods in sklearn.

I am also not sure about what the method
reduced_likelihood_function(theta) actually computes. I tried to combine
that likelihood with a prior to choose the kernel parameters via
MAP-estimation and didn't get reasonable results (computing the marginal
likelihood as discussed on page 113 of the Rasmussen & Williams book and
combining that with a prior fixed the issue). The documentation is also
quite unclear on how the reduced-likelihood is connected to the marginal
likelihood (if at all)

Best,
Jan

On 25.11.2014 18:37, Andy wrote:
> There are definitely API questions that I also just discusses with Dan.
> There are some thing that we could improve, but I think the solutions 
> depend a lot on if we want to do kernel engineering or not.
> My thinking was that this part is probably the most controversial one, 
> so this is what I asked about.
>
> I am not sure how useful our current implementation is. I have not met a 
> person that uses it.
> That might be caused by the interface and missing documentation more 
> than by the fact that we don't have custom kernels, though.
>
> I don't think we want to add a HODLR solver (hierarchical off-diagonal 
> low-rank solver).
> It you want that, you should probably install gorge ;)
>
> What I think would be great to have is gradient based optimization of 
> the kernel parameters, and a way to do grid-search
> using data likelihood (not sure if that is currently supported).
>
> For the API, the naming is somewhat non-standard, it is not super clear 
> what the parameters mean, and it is also not super clear
> whether the kernel-parameters will be optimized for a given parameters 
> setting.
>
>
>
>
> On 11/25/2014 12:28 PM, Gael Varoquaux wrote:
>> On Tue, Nov 25, 2014 at 12:23:50PM -0500, Kyle Kastner wrote:
>>> specifically a HODLR solver.
>> What is this. Can you tell us more?
>>
>>> One very specific reason to focus on GP code quality would be that it
>>> opens the door to use sklearn's own code to implement some very nice
>>> hyperparameter search algorithms which could be useful to many users.
>> Yes. I pretty badly would like this (Kyle, are you looking for an
>> internship? You know, France is nice :P).
>>
>> Gaël
>>
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-- 
 Jan Hendrik Metzen,  Dr.rer.nat.
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