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Update svm.rst
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‎doc/modules/cross_validation.rst

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@@ -200,7 +200,7 @@ section.
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* :ref:`example_feature_selection_plot_rfe_with_cross_validation.py`,
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* :ref:`example_model_selection_grid_search_digits.py`,
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* :ref:`example_model_selection_grid_search_text_feature_extraction.py`,
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* :ref:`example_plot_cv_predict.py`,
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* :ref:`example_plot_cv_predict.py`.
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Cross validation iterators
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==========================
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When compared with :math:`k`-fold cross validation, one builds :math:`n` models
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from :math:`n` samples instead of :math:`k` models, where :math:`n > k`.
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Moreover, each is trained on :math:`n - 1` samples rather than
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:math:`(k-1)n / k`. In both ways, assuming :math:`k` is not too large
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:math:`(k-1) n / k`. In both ways, assuming :math:`k` is not too large
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and :math:`k < n`, LOO is more computationally expensive than :math:`k`-fold
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cross validation.
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.. topic:: References:
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* http://www.faqs.org/faqs/ai-faq/neural-nets/part3/section-12.html
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* `<http://www.faqs.org/faqs/ai-faq/neural-nets/part3/section-12.html>`_;
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* T. Hastie, R. Tibshirani, J. Friedman, `The Elements of Statistical Learning
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<http://www-stat.stanford.edu/~tibs/ElemStatLearn>`_, Springer 2009
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<http://www-stat.stanford.edu/~tibs/ElemStatLearn>`_, Springer 2009;
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* L. Breiman, P. Spector `Submodel selection and evaluation in regression: The X-random case
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<http://digitalassets.lib.berkeley.edu/sdtr/ucb/text/197.pdf>`_, International Statistical Review 1992
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<http://digitalassets.lib.berkeley.edu/sdtr/ucb/text/197.pdf>`_, International Statistical Review 1992;
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* R. Kohavi, `A Study of Cross-Validation and Bootstrap for Accuracy Estimation and Model Selection
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<http://www.cs.iastate.edu/~jtian/cs573/Papers/Kohavi-IJCAI-95.pdf>`_, Intl. Jnt. Conf. AI
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<http://www.cs.iastate.edu/~jtian/cs573/Papers/Kohavi-IJCAI-95.pdf>`_, Intl. Jnt. Conf. AI;
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* R. Bharat Rao, G. Fung, R. Rosales, `On the Dangers of Cross-Validation. An Experimental Evaluation
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<http://www.siam.org/proceedings/datamining/2008/dm08_54_Rao.pdf>`_, SIAM 2008
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<http://www.siam.org/proceedings/datamining/2008/dm08_54_Rao.pdf>`_, SIAM 2008;
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* G. James, D. Witten, T. Hastie, R Tibshirani, `An Introduction to
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Statistical Learning <http://www-bcf.usc.edu/~gareth/ISL>`_, Springer 2013
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Statistical Learning <http://www-bcf.usc.edu/~gareth/ISL>`_, Springer 2013.
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Leave-P-Out - LPO
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Each training set is thus constituted by all the samples except the ones
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related to a specific label.
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For example, in the cases of multiple experiments, *LOLO* can be used to
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For example, in the cases of multiple experiments, LOLO can be used to
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create a cross-validation based on the different experiments: we create
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a training set using the samples of all the experiments except one::
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.. warning::
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Contrary to :class:`StratifiedKFold`, the ``labels`` of
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:class:`LeaveOneLabelOut` should not encode the target class to predict:
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the goal of :class:`StratifiedKFold` is to rebalance dataset classes across
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Contrary to :class:`StratifiedKFold`,
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the ``labels`` of :class:`LeaveOneLabelOut` should not encode
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the target class to predict: the goal of :class:`StratifiedKFold`
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is to rebalance dataset classes across
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the train / test split to ensure that the train and test folds have
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approximately the same percentage of samples of each class while
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:class:`LeaveOneLabelOut` will do the opposite by ensuring that the samples

‎doc/modules/svm.rst

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@@ -238,7 +238,7 @@ and use ``decision_function`` instead of ``predict_proba``.
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* Wu, Lin and Weng,
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`"Probability estimates for multi-class classification by pairwise coupling"
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<http://www.csie.ntu.edu.tw/~cjlin/papers/svmprob/svmprob.pdf>`_.
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<http://www.csie.ntu.edu.tw/~cjlin/papers/svmprob/svmprob.pdf>`_,
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JMLR 5:975-1005, 2004.
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* **Avoiding data copy**: For :class:`SVC`, :class:`SVR`, :class:`NuSVC` and
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:class:`NuSVR`, if the data passed to certain methods is not C-ordered
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contiguous, and double precision, it will be copied before calling the
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underlying C implementation. You can check whether a give numpy array is
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underlying C implementation. You can check whether a given numpy array is
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C-contiguous by inspecting its ``flags`` attribute.
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For :class:`LinearSVC` (and :class:`LogisticRegression
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where :math:`e` is the vector of all ones, :math:`C > 0` is the upper bound,
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:math:`Q` is an :math:`n` by :math:`n` positive semidefinite matrix,
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:math:`Q_{ij} \equiv y_i y_j K(x_i, x_j)` Where :math:`K(x_i, x_j) = \phi (x_i)^T \phi (x_j)`
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:math:`Q_{ij} \equiv y_i y_j K(x_i, x_j)`, where :math:`K(x_i, x_j) = \phi (x_i)^T \phi (x_j)`
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is the kernel. Here training vectors are implicitly mapped into a higher
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(maybe infinite) dimensional space by the function :math:`\phi`.
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.. topic:: References:
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* `"Automatic Capacity Tuning of Very Large VC-dimension Classifiers"
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<http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.17.7215>`_
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I Guyon, B Boser, V Vapnik - Advances in neural information
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processing 1993,
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<http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.17.7215>`_,
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I. Guyon, B. Boser, V. Vapnik - Advances in neural information
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processing 1993.
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* `"Support-vector networks"
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<http://www.springerlink.com/content/k238jx04hm87j80g/>`_
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C. Cortes, V. Vapnik, Machine Leaming, 20, 273-297 (1995)
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<http://www.springerlink.com/content/k238jx04hm87j80g/>`_,
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C. Cortes, V. Vapnik - Machine Learning, 20, 273-297 (1995).
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.. topic:: References:
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* `"A Tutorial on Support Vector Regression"
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<http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.114.4288>`_
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Alex J. Smola, Bernhard Schölkopf -Statistics and Computing archive
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Volume 14 Issue 3, August 2004, p. 199-222
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<http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.114.4288>`_,
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Alex J. Smola, Bernhard Schölkopf - Statistics and Computing archive
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Volume 14 Issue 3, August 2004, p. 199-222.
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.. _svm_implementation_details:
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used, please refer to
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- `LIBSVM: a library for Support Vector Machines
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<http://www.csie.ntu.edu.tw/~cjlin/papers/libsvm.pdf>`_
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<http://www.csie.ntu.edu.tw/~cjlin/papers/libsvm.pdf>`_.
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- `LIBLINEAR -- A Library for Large Linear Classification
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<http://www.csie.ntu.edu.tw/~cjlin/liblinear/>`_
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- `LIBLINEAR -- a library for Large Linear Classification
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<http://www.csie.ntu.edu.tw/~cjlin/liblinear/>`_.
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