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improved sobol docs
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claesenm committed May 16, 2015
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Expand Up @@ -4,15 +4,21 @@ Sobol sequences
.. include:: /global.rst

A Sobol sequence is a low discrepancy quasi-random sequence. Sobol sequences were designed to cover the unit
hypercube with lower discrepancy than completely random sampling (e.g. |random-search|). Optunity supports Sobol
hypercube with lower discrepancy than completely random sampling (e.g. |randomsearch|). Optunity supports Sobol
sequences in up to 40 dimensions (e.g. 40 hyperparameters).

The figures below show the differences between a Sobol sequence and sampling uniformly at random.

.. figure:: sobol.png
:alt: Points sampled in 2D with a Sobol sequence.
:alt: 100 points sampled in 2D with a Sobol sequence.

100 points sampled in 2D with a Sobol sequence.



.. figure:: random.png
:alt: Points sampled in 2D uniformly at random.
:alt: 100 points sampled in 2D uniformly at random.

100 points sampled in 2D uniformly at random.

The mathematical details on Sobol sequences are available in the following papers: [SOBOL]_, [ANTONOV]_, [BRATLEY]_, [FOX]_.

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