What kernel methods in sklearn don't accept precomputed kernels? I'm not sold on this because it's really hacky. I have not heard of anyone do that. Can you give an example when you'd do that?

I do this because the objects in my x space are molecules. My kernel is Tanimoto similarity between molecule fingerprints.

The point of kernel methods is that devising an appropriate kernel function is an alternative to feature extraction. Mercer's theorem says that a kernel induces a vector space over the input space, but an infinite-dimensional one, so this approach is inherently more powerful than identifying features. Reducing the input space to a vector of features then choose a kernel function is missing the point.

To repeat: What kernel methods in sklearn don't accept precomputed kernels?

Tanimoto similarity is the jaccard similarity, right? That doesn't lead to a positive definite kernel?

Hm I guess it does not, but wouldn't exp(similarity) lead to one?

To repeat: What kernel methods in sklearn don't accept precomputed kernels?

Gaussian Process Regression.

For Kernel Ridge Regression, just a documentation change is needed.

For Kernel Ridge Regression does not mention it, but in fact it supports

animoto similarity is the jaccard similarity, right? That doesn't lead to a positive definite kernel?

"It is well known that the Jaccard–Tanimoto similarity measure satisfies the Mercer's conditions and, hence, yields a Mercer kernel "
https://academic.oup.com/bioinformatics/article/26/10/1348/193672

Ok, so you don't need to "coerce the Gram matrix". I had asked when you need to coerce the gram matrix and you gave that as an example.

Hi Chris, a bigger problem (but related I think) is that currently scikit-learn doesn't implement the Tanimoto kernel. While this kernel is super useful in cheminformatics and information research and not everybody is skilled enough to contribute to scikit-learn. Cf. #29507 I am unsure if Tanimoto kernel would be unsuited to kernel-based methods, but @jpvert might know.