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Add cauchy kernel cookbook #4338

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merged 4 commits into from Jun 20, 2018

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vinx13 commented Jun 16, 2018

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karlnapf commented Jun 19, 2018

Thanks for this!

As said a few times before, let's not have more kernel cookbooks (after this one) as we already have tons of them. Rather, we should have cookbooks for algorithms that haven't been described yet

Cauchy Kernel
=============
The cauchy kernel is derived from the Cauchy distribution :cite:`basak2008kernel`. It is a long-tailed kernel defined as

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karlnapf Jun 19, 2018

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Minor: pls start new sentences in a new line

The cauchy kernel is derived from the Cauchy distribution :cite:`basak2008kernel`. It is a long-tailed kernel defined as
.. math::
K(x,x') = \frac{1}{1+\frac{\| x-x' \|^2}{\sigma}}

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I would prefer a lowercase k, unless K is used elsewhere

@@ -96,6 +96,16 @@ Distance
examples/distance/**
Kernel

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karlnapf Jun 19, 2018

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oh wait, we didnt have kernels yet? ;)
Ok then this is quite good to have :)

@@ -163,3 +163,10 @@ @article{hyvarinen2000independent
pages={411--430},
year={2000}
}
@inproceedings{basak2008kernel
author={J. Basak},
booktitle={2008 19th International Conference on Pattern Recognition},

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karlnapf Jun 19, 2018

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is this really the best reference? where do you have it from? can't we use some of the references we already used (like the kernel book by schölkopf?)

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vinx13 Jun 19, 2018

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i found several links point to this paper, e.g https://github.com/gmum/pykernels/blob/c8afdc79a15197ad3be2a0db0118f5e948577f49/pykernels/regular.py#L132
and I've checked that paper, the author gave a definition of it in sec.3

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karlnapf Jun 20, 2018

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ok cool. When citing it, put [Section 3] in there (if possible)

booktitle={2008 19th International Conference on Pattern Recognition},
title={A least square kernel machine with box constraints},
year={2008},
pages={1-4},

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karlnapf Jun 19, 2018

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pls do proper references. These pages here are definitely not correct

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vinx13 Jun 19, 2018

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ICPR papers are not re-assigned a page number when they are published. This is based on the reference format provided in https://ieeexplore.ieee.org/document/4761717

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karlnapf Jun 20, 2018

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I see, maybe we can remove them then?

We create an instance of :sgclass:`CCauchyKernel`.
.. sgexample:: cauchy:create_kernel

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karlnapf Jun 19, 2018

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Could you talk about the fact that a distance is used for this kernel?

vinx13 added some commits Jun 19, 2018

@karlnapf

ok from my side

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karlnapf commented Jun 20, 2018

I restarted windows since it was failing

@@ -167,6 +167,5 @@ @inproceedings{basak2008kernel
author={J. Basak},
booktitle={2008 19th International Conference on Pattern Recognition},
title={A least square kernel machine with box constraints},
year={2008},
pages={1-4},
year={2008}

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karlnapf Jun 20, 2018

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cool thx!

Did you render this locally (the html output) and check that it all works ?

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vinx13 Jun 20, 2018

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Yes it works

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karlnapf commented Jun 20, 2018

Alright, great! thanks!

@karlnapf karlnapf merged commit c870b67 into shogun-toolbox:develop Jun 20, 2018

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