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add docs for interpretation of length scales in periodic kernel #3989

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merged 4 commits into from
Jul 17, 2020
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add docs for interpretation of length scales in periodic kernel #3989

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7c9a3be
fix the expression of periodic kernel
tirthasheshpatel Jul 1, 2020
1b4491e
revert change and add doc
tirthasheshpatel Jul 7, 2020
155ef1e
FIXUP: add suggested doc string
tirthasheshpatel Jul 13, 2020
cec9755
FIXUP: revertchanges in .gitignore
tirthasheshpatel Jul 13, 2020
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1 change: 1 addition & 0 deletions .gitignore
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Expand Up @@ -41,3 +41,4 @@ benchmarks/results/
pytestdebug.log
.dir-locals.el
.pycheckers
env/
9 changes: 9 additions & 0 deletions pymc3/gp/cov.py
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Expand Up @@ -353,6 +353,15 @@ class Periodic(Stationary):

.. math::
k(x, x') = \mathrm{exp}\left( -\frac{\mathrm{sin}^2(\pi |x-x'| \frac{1}{T})}{2\ell^2} \right)

The interpretation of length-scale for this kernel is different than the
one used normally (see [1]_). Priors on length scale must be put keeping
this in mind.
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Suggested change
The interpretation of length-scale for this kernel is different than the
one used normally (see [1]_). Priors on length scale must be put keeping
this in mind.
The scaling factor for this kernel is different compare to the other standard
definition (see [1]_), thus change the interpretation of length-scale in a subtle
way. Please keep that in mind when you are defining priors on length scale,
especially when you are trying to replicate other results.
You can divided the length-scale by 2 in the kernel initialization to recover the
standard definition.

@bwengals is this correct?

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@bwengals bwengals Jul 9, 2020 •
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If I read that it's different, how should one interpret it? I think it'd be good to be specific.

Also small wording suggestion, how does this sound?

Note that the scaling factor for this kernel is different compared to the more common definition (see [1]_). Here, 0.5 is in the exponent instead of the more common value, 4. Divide the length-scale by 2 when initializing the kernel to recover the standard definition.

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Sorry for not replying earlier. I missed @bwengals's reply.

Here, 0.5 is in the exponent instead of the more common value, 4.

I think what you meant here was:

Here, 0.5 is in the exponent instead of the more common value, 2.

Right?

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whoops, yep you're right!


References
----------
.. [1] David Duvenaud, "The Kernel Cookbook"
https://www.cs.toronto.edu/~duvenaud/cookbook/
"""

def __init__(self, input_dim, period, ls=None, ls_inv=None, active_dims=None):
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