Kernel wishlist: categorical variants and other useful kernels

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?

No files, tests, or implementation entry points are named. Start by narrowing the wishlist to one proposed categorical or continuous kernel, then review the existing kernel implementations and determine the expected parameterization and validation. Done should mean a specific kernel is selected with an agreed implementation scope.