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[MRG] Fix math syntax for ComplementNB documentation. #9644

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Aug 29, 2017
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[MRG] Fix math syntax for ComplementNB documentation. #9644

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c7f744a
Fix ComplementNB documentation math syntax.
airalcorn2 Aug 29, 2017
36ea0b7
Break long line in two
lesteve Aug 29, 2017
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21 changes: 12 additions & 9 deletions doc/modules/naive_bayes.rst
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Original file line number Diff line number Diff line change
Expand Up @@ -136,7 +136,7 @@ while :math:`\alpha < 1` is called Lidstone smoothing.
.. _complement_naive_bayes:

Complement Naive Bayes
-----------------------
----------------------

:class:`ComplementNB` implements the complement naive Bayes (CNB) algorithm.
CNB is an adaptation of the standard multinomial naive Bayes (MNB) algorithm
Expand All @@ -149,20 +149,23 @@ calculating the weights is as follows:

.. math::

\hat{\theta}_{ci} = \frac{\sum{j:y_j \neq c} d_{ij} + \alpha_i}
{\sum{j:y_j \neq c} \sum{k} d_{kj} + \alpha}
\hat{\theta}_{ci} = \frac{\alpha_i + \sum_{j:y_j \neq c} d_{ij}}
{\alpha + \sum_{j:y_j \neq c} \sum_{k} d_{kj}}

w_{ci} = \log \hat{\theta}_{ci}
w_{ci} = \frac{w_{ci}{\sum{j} w_{cj}}

where the summation is over all documents :math:`j` not in class :math:`c`,
w_{ci} = \frac{w_{ci}}{\sum_{j} w_{cj}}

where the summations are over all documents :math:`j` not in class :math:`c`,
:math:`d_{ij}` is either the count or tf-idf value of term :math:`i` in document
:math:`j`, and :math:`\alpha` is a smoothing hyperparameter like that found in
MNB. The second normalization addresses the tendency for longer documents to
dominate parameter estimates in MNB. The classification rule is:
:math:`j`, :math:`\alpha_i` is a smoothing hyperparameter like that found in
MNB, and :math:`\alpha = \sum_{i} \alpha_i`. The second normalization addresses
the tendency for longer documents to dominate parameter estimates in MNB. The
classification rule is:

.. math::

\hat{c} = \arg\min_c \sum{i} t_i w_{ci}
\hat{c} = \arg\min_c \sum_{i} t_i w_{ci}

i.e., a document is assigned to the class that is the *poorest* complement
match.
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