ENH: Improving GP models #244
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@jhlegarreta our simulated data may not be realistic enough for our tests:
That said, convergence issues also happen when using b=3000 of HCP. |
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@jhlegarreta @yasseraleman -- I may have found the potential culprit that makes fitting so weird. By looking at the covariance vs. angle plots (at the beginning of the notebook), I ended up realizing that they massaged the data before calculating the covariance. They certainly removed the mean (I don't know if gradient-wise mean or the grand mean), and possibly scaled to one-standard-deviation. Then I went back to the paper and found the little comment I included in the docstring of ``EddymotionGPR.fit()``. This doesn't completely resolve all problems, but I'm positive it's one little step we needed to take.
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@jhlegarreta @yasseraleman -- the new plot accounting for the normalization of the data differently (see my commit message in 3136256):
Perhaps the optimizer is moving a towards |
@oesteban 🎉 looks reasonable.
Maybe I'm being very naive, but they assume that Maybe since they add it back to the predictions when writing the volumes as they have kept track of the value. But have not found the place, unless it is this one: |
I don't think that's naive and I understand the same of the text. But then the question is you can obtain |
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Addendum: This would invalidate our cross-validation unless we regress data to |
It seems I was wrong about the need for standardizing, Scikit-learn's
implementation is sufficient and follows what the paper specifies.
There are a few additional details that have surfaced as relevant:
* $\sigma^2$ should not be very large (and ~100) was VERY large.
With small values, it seems to pacify optimizers with more plausible
outcomes.
* $a$ may take values above $\frac{\pi}{2}$, even though $\theta$ will
always be smaller than that.
Indeed, it seems for our real dataset the optimal $a$ is indeed around
$\frac{\pi}{2}$.
* I haven't cracked the manipulations of the covariance plot yet, but
it's clear to me now that they are indeed considering $a$ and $\lambda$.
The most relevant inclusion in this commit is the repetition of the
covariance plot with the covariance of predicted data, which is very
encouraging.
cc @jhlegarreta.
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It occurred to me that we could plot the covariance of predictions (out of sample, btw):
Promising! (see updated notebook) |
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Improved: |
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