pymc.gp.util.stabilize is broken

[fonnesbeck]

Describe the issue:

Wrapping a covariance function with stabilize causes a failure. Not sure why it is expecting a tensor variable.

Reproduceable code example:

import pymc as pm
import numpy as np

with pm.Model() as m:

    K = pm.gp.util.stabilize(pm.gp.cov.ExpQuad(input_dim=1, ls=1))

    gp = pm.gp.Latent(cov_func=K)

    f = gp.prior('f', X = np.random.randn(10)[:, None])

    y = pm.Normal('y', mu=f, sigma=1, observed=np.random.randn(10))

Error message:

NotImplementedError: Cannot convert <pymc.gp.cov.ExpQuad object at 0x7fdd378246d0> to a tensor variable.

### PyMC version information:

PyMC 5.10

### Context for the issue:

_No response_

[hchen19]

Hi, the stabilize function adds a diagonal to a matrix K by using pytensor.tensor.identity_like(K), so the input of stabilize should be a matrix, not a function. Therefore, it should be implemented as follows:

import pymc as pm
import numpy as np

with pm.Model() as m:'
    X = np.random.randn(10)[:, None]
    cov_fun = pm.gp.cov.ExpQuad(input_dim=1, ls=1)
    K = pm.gp.util.stabilize(cov_fun(X))

    gp = pm.gp.Latent(cov_func=K)

    f = gp.prior('f', X)

    y = pm.Normal('y', mu=f, sigma=1, observed=np.random.randn(10))

Plus, I don't think you need to stabilize the covariance matrix before using gp.Latent, since gp.prior already applies stabilize to the covariance matrix, you don't need to apply it again.