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implement GP-LVM from scratch #1009

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implement GP-LVM from scratch#1009
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karm-patel

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@murphyk
murphyk
opened on Jul 17, 2022

Currently fig 28.19 is created by https://github.com/probml/pyprobml/blob/master/notebooks/book2/28/gplvm_mocap.ipynb
which uses GPy from Sheffield.
Here is the core code

model = GPy.models.GPLVM(Y, 2, init="PCA", normalizer=True)
model.optimize(optimizer="lbfgs", messages=True, max_f_eval=1e4, max_iters=1e4)

It would be useful to reimplement this from first principles, using eg TinyGP to define the Gram matrix.

Screen Shot 2022-07-17 at 10 10 03 AM

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  1. murphyk
    assigned
    karm-patel
    on Jul 17, 2022

  2. murphyk commented on Jul 17, 2022

    @murphyk
    murphyk
    on Jul 17, 2022
    MemberAuthor

    BTW I slightly rewrote the section n GPLVM (28.3.7) to make the notation clearer. New version below.
    Screen Shot 2022-07-17 at 10 36 52 AM

    I found this colab (based on PyMc4 , which uses TFP and is deprecated) that fits the GP-LVM model using ADVI to the iris dataset.
    https://colab.research.google.com/drive/1BhqYin-3W1bmGgNxA95HKZZw3ACmicRK?usp=sharing
    (They use a NormalCholesky prior on the latent inputs Z/X.) When using a linear kernel you get the same results as PCA (modulo rotation). This would be a good example to try to reproduce.
    (It seems from this thread that the code was never merged, presumably because pymc4 is deprecated.)

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