Kernel wishlist: categorical variants and other useful kernels

[bwengals]

Collecting ideas for new kernels. ptgp currently ships:

Stationary: ExpQuad, Matern52, Matern32, Matern12
Categorical: Overlap, LowRankCategorical
Non-stationary: RandomWalk, Gibbs, WarpedInput

Categorical kernels

There's a lot of room to grow here. Some ideas:

• FullCategorical — a full-rank PSD level covariance matrix, parameterized via pm.LKJCholeskyCov or a user-supplied PSD matrix. Proper LKJ prior on the level correlation structure.
• LowRankCategorical identifiability fixes — the current eta**2 * LowRankCategorical(W, kappa) has a scalar non-identifiability (eta and W/kappa can trade scale). Diagonal normalization (force unit diagonal on B, delegate all amplitude to eta) is the intended structural fix.
• GroupedCategorical — sum or product of per-column ICM kernels for rows with multiple categorical features (e.g. country, device type, experiment arm). Mostly sugar over composing LowRankCategorical instances, but the parameter setup gets repetitive without it.
• HierarchicalCategorical — for nested categorical columns (country > region > city). Covariance is a sum where each level's contribution is gated by shared ancestry. Sharing across related groups regularizes sparse leaves.

Continuous kernels

What other continuous kernels would be useful? Some starting points:

• Periodic / locally periodic
• Spectral mixture
• Polynomial
• Linear
• Changepoint / switching kernels
• Rational quadratic

Open questions

• What other kernels are people using that would be worth adding?
• Are there kernels that would be useful but are tricky to implement or experiment with?