Make GP latent vs marginal test deterministic

[Jiya873]

Fixes #8000

[maresb]

Looks good @Jiya873 ! Could you please share the seed you found that makes this fail? That would be useful to note for reference.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 91.49%. Comparing base (cadb97a) to head (756e02b).

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #8006      +/-   ##
==========================================
+ Coverage   90.22%   91.49%   +1.27%     
==========================================
  Files         116      116              
  Lines       18972    18972              
==========================================
+ Hits        17117    17359     +242     
+ Misses       1855     1613     -242     

see 5 files with indirect coverage changes

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[Jiya873]

First, I created a reproduction script and found that the assertion fails immediately at the first iteration.

import numpy as np
import pymc as pm
import pytensor.tensor as pt
import numpy.testing as npt
from tqdm import tqdm

def run_reproduction(seed):
    rng = np.random.RandomState(seed)
    n_outputs = 2
    X = rng.randn(20, 3)
    y = rng.randn(n_outputs, 20)
    Xnew = rng.randn(30, 3)
    pnew = rng.randn(n_outputs, 30)

    with pm.Model() as latent_model:
        cov_func = pm.gp.cov.ExpQuad(3, [0.1, 0.2, 0.3])
        mean_func = pm.gp.mean.Constant(0.5)
        latent_gp = pm.gp.Latent(mean_func=mean_func, cov_func=cov_func)
        latent_f = latent_gp.prior("f", X, n_outputs=n_outputs, reparameterize=True)
        latent_p = latent_gp.conditional("p", Xnew)

    with pm.Model() as marginal_model:
        cov_func = pm.gp.cov.ExpQuad(3, [0.1, 0.2, 0.3])
        mean_func = pm.gp.mean.Constant(0.5)
        marginal_gp = pm.gp.Marginal(mean_func=mean_func, cov_func=cov_func)

        marginal_f = marginal_gp.marginal_likelihood("f", X, y, sigma=0.0)
        marginal_p = marginal_gp.conditional("p", Xnew)

    lp_latent = latent_p.eval({latent_f: y})
    lp_marginal = marginal_p.eval()

    npt.assert_allclose(lp_latent, lp_marginal, rtol=1e-4)

if __name__ == "__main__":
    iterations = 500    
    for i in tqdm(range(iterations)):
        try:
            run_reproduction(seed=i)
        except AssertionError as e:
            print(f"\nCaught failure at seed: {i}")
            print(e)
            break

I reproduced the failure locally using seed 0.