Sequential calls to predict using VFE and SVGP models

[tadejkrivec]

I already posted this under another issue. I have an example where I have to call predict sequentially. Why would SVGP predictions be faster then SGPR in that case? Isn't the time complexity with prediction the same for all sparse models or am I missing something? This is the code I ran for testing it:

from numpy.random import randn
import gpflow

sgpr = gpflow.models.SGPR(X=randn(70000,8), Y=randn(70000,1), kern=gpflow.kernels.SquaredExponential(8), Z=randn(200,8))
sgpr.predict_y(randn(1,8))
%timeit -n 100 -r 7 sgpr.predict_y(randn(1,8))
>>> 128 ms ± 696 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)

svgp = gpflow.models.SVGP(X=randn(70000,8), Y=randn(70000,1), kern=gpflow.kernels.SquaredExponential(8), likelihood=gpflow.likelihoods.Gaussian(), Z=randn(200,8))
svgp.predict_y(randn(1,8))
%timeit -n 100 -r 7 svgp.predict_y(randn(1,8))
>>> 6.61 ms ± 913 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)

[st--]

@tadejkrivec sorry for the late answer, I believe it's because of the lack of storing the pre-computed matrices -- the SGPR model in predict_y still operates on the 70000-row X and Y vectors (computing exactly) each time, whereas SVGP has stored that information ("approximately") in the q(u) distribution which is much smaller. "Time complexity" just means whether it's O(NM^2 + M^3), doesn't say anything about the prefactor... Really, this would be long better on stackoverflow.com (tag gpflow: https://stackoverflow.com/questions/tagged/gpflow), if you would be up for posting your question again there I'll add my answer there and future users can come across it too. Thanks!

[tadejkrivec]

I've posted the question on Stackoverflow. I did figure that on my own. My workaround is a custom implementation for prediction where I precompute the part of the graph dependent on the training dataset and then reuse it in a loop.

[st--]

Feel free to answer it yourself then! :)

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On Wed, 4 Dec 2019 at 08:05, tadejkrivec ***@***.***> wrote: I've posted the question on Stackoverflow. I did figure that on my own. My workaround is a custom implementation for prediction where I precompute the part of the graph dependent on the training dataset and then reuse it in a loop. — You are receiving this because you modified the open/close state. Reply to this email directly, view it on GitHub <#1030?email_source=notifications&email_token=ABL7FD3Y24KKYUOXDREKAFTQW5QEVA5CNFSM4IOGGKYKYY3PNVWWK3TUL52HS4DFVREXG43VMVBW63LNMVXHJKTDN5WW2ZLOORPWSZGOEF4C64A#issuecomment-561524592>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/ABL7FD2USRYG4EJQX4AYFITQW5QEVANCNFSM4IOGGKYA> .