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I am trying to implement GP regression using Poisson likelihood. I followed the example in GPy by doing

poisson_likelihood = GPy.likelihoods.Poisson()
laplace_inf = GPy.inference.latent_function_inference.Laplace()
m = GPy.core.GP(X=X, Y=Y, likelihood=poisson_likelihood, inference_method=laplace_inf, kernel=kernel)
m.optimize()
#for ploting
pred_points = np.linspace(300,800,1000)[:, None]
#Predictive GP for log intensity mean and variance
f_mean, f_var = m._raw_predict(pred_points)
f_upper, f_lower = f_mean + 2*np.sqrt(f_var), f_mean - 2.*np.sqrt(f_var)
pb.figure(figsize=(10, 13))
pb.plot(pred_points, np.exp(f_mean), color='blue', lw=2)
pb.fill_between(pred_points[:,0], np.exp(f_lower[:,0]), np.exp(f_upper[:,0]), color='blue', alpha=.1)
pb.errorbar(Xc.flatten(), Yc.flatten(), dyc, fmt='.', color='k',markersize=8,alpha=1.0, label='Data')

When I tried to do the same using GPflow, I implemented in the following way

poisson_likelihood = gpflow.likelihoods.Poisson()
m = gpflow.models.VGP((X, Y), kernel=k, likelihood=poisson_likelihood, num_latent_gps=1)
opt = gpflow.optimizers.Scipy()
opt_logs = opt.minimize(m.training_loss, m.trainable_variables, options=dict(maxiter=100))
#for ploting
xx = np.linspace(300, 800, 100).reshape(100, 1)
mean, var = m.predict_f(xx)
plt.plot(X, Y, "kx", mew=2)
plt.plot(xx, np.exp(mean), "C0", lw=2)
plt.fill_between(
    xx[:, 0],
    np.exp(mean[:, 0] - 1.96 * np.sqrt(var[:, 0])),
    np.exp(mean[:, 0] + 1.96 * np.sqrt(var[:, 0])),
    color="C0",
    alpha=0.2,
)

When I implemented this using GP flow, the hyper parameters did not move from initialized values. Also, I am getting very different results, am I doing something wrong?

Result with GPflow

Result with GPy

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    It's hard to help figuring out why it might not work as expected without it being a minimal reproducible example. Note that in GPy, you are using Laplace approximation, whereas in GPflow you are using a variational approximation - though I would expect the hyperparameters to move in the latter, too. Commented Feb 28, 2022 at 11:08
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