Stochastic Lanczos for log determinant computation

[rmassidda]

Hi there! 👋

I am trying to reproduce the use of stochastic Lanczos over SKI, as in "Scalable Log Determinants for Gaussian Process Kernel Learning" (Dong et al., 2017). I see that GPyTorch provides an implementation in utils.StochasticLQ, but it's nowhere referenced in the codebase anymore.

If I correctly understood the workflow, I should extend InterpolatedLazyTensor and redefine inv_quad_logdet to use stochastic Lanczos. Then, I should derive a new kernel class from GridInterpolationKernel that adopts the newly defined lazy tensor.

Does it make sense? If not, could someone give me some hints? 🙏

[wjmaddox]

It should be used automatically inside of inv_quad_logdet (via _inv_quad_logdet). See the code at

gpytorch/gpytorch/functions/_inv_quad_logdet.py

Line 139 in 306d733

if settings.skip_logdet_forward.off():

. Although now the procedure isn't quite that of Dong et al, but rather a variance reduced method introduced in https://arxiv.org/abs/2107.00243.

[rmassidda]

Thanks, it's clear now. :)