MCMC prediction stability issue - providing NAN values of variance (Issue in Google Colab GPU/HighRam setting)

[arpanbiswas52]

**This is the issue encountered in Google Colab- under GPU setting T4 and High-RAM

When we run the function- ExactGP.fit()-- it produces NAN values for standard deviation calculation. The error can be repo in all the below modifications These things I have already tried

• Normalize the data in fitting the model
• Tried with all the kernels: RBF, Matern and Periodic
• Tried with diff prior function: LogNormal, Normal, HalfNormal which are mostly used anyway in GP/BO
• Tried with diff noise priors
• Also tried with diff sets of training data

With current workaround it seems with reducing the number of total samples in MCMC setting to num_warmup=500, num_samples=500 (Default is num_warmup=1000, num_samples=3000), it is able to provide reasonable outputs.

[nmenon97]

Encountered the same issue without using Google Colab or GPU

[ziatdinovmax]

@nmenon97 - did it happen in the 64-bit precision regime?

[nmenon97]

@ziatdinovmax yes! I can sometimes get it to work by changing num_warmup and num_samples as suggested above but it isn't a stable solution.

[ziatdinovmax]

This is due to the peculiar behavior of jax.vmap when approaching a memory limit. There are three ways to deal with this:

1. Draw multiple random smaller batches of samples (see gpax.acquisition.qEI, .qUCB, etc; you can specify the batch size using the subsample_size argument) and average them.
2. Assume that the acquisition function is continuous and use gpax.acquisition.optimize_acq to optimize it with num_initial_guesses << total_number_of_points.
3. Use a device with a larger memory :)