CODEWITHSUNDEEP
python-3.xtensorflowmachine-learninggaussiangpflow
Mo Abdolhosseini Moghaddam
Mo Abdolhosseini Moghaddam

Reputation: 51

Can kernels other than periodic be used in SGPR in gpflow

I am pretty new to GPR. I will appreciate it if you provide me some suggestion regarding the following questions:

Can we use the Matern52 kernel in a sparse Gaussian process?

What is the best way to select pseudo inputs (Z) ? Is random sampling reasonable?

I would like to mention that when I am using the Matern52 kernel, the following error stops optimization process. My code:

k1 = gpflow.kernels.Matern52(input_dim=X_train.shape[1], ARD=True)
m = gpflow.models.SGPR(X_train, Y_train, kern=k1, Z=X_train[:50, :].copy())

InvalidArgumentError (see above for traceback): Input matrix is not invertible. [[Node: gradients_25/SGPR-31ceaea6-412/Cholesky_grad/MatrixTriangularSolve = MatrixTriangularSolve[T=DT_DOUBLE, adjoint=false, lower=true, _device="/job:localhost/replica:0/task:0/device:CPU:0"](SGPR-31ceaea6-412/Cholesky, SGPR-31ceaea6-412/eye_1/MatrixDiag)]

Any help will be appreciated, thank you.

Upvotes: 1

Views: 244

Answers (1)

STJ
STJ

Reputation: 1537

Have you tried it out on a small test set of data, that you could perhaps post here? There is no reason Matern52 shouldn't work. Randomly sampling inducing points should be a reasonable initialisation, especially in higher dimensions. However, you may run into issues if you end up with some inducing points very close to each other (this can make the K_{zz} = cov(f(Z), f(Z)) matrix badly conditioned, which would explain why the Cholesky fails). If your X_train isn't already shuffled, you may want to use Z=X_train[np.random.permutation(len(X_train))[:50] to get shuffled indices. It may also help to add a white noise kernel, kern=k1+gpflow.kernels.White() ...

Upvotes: 1

Related Questions