How to reverse GP-LVM Gaussian process latent variable and reconstruct original variables using python?

Question

GP-LVM an be used for dimensionality reduction. After such dimensionality reduction is performed, how can one approximately reconstruct the original variables/features?

Answer 1

Using GPy, you can use the predict function, which returns the predictive mean and variance:

import numpy as np
from   GPy.models import GPLVM

m = GPLVM(Y, input_dim=2)
m.optimize()
mean, var = m.predict(m.X)
print(np.linalg.norm(Y - mean, 2))