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271 lines
12 KiB
ReStructuredText
271 lines
12 KiB
ReStructuredText
.. _Gradient Boosted Trees:
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Gradient Boosted Trees
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======================
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.. highlight:: cpp
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Gradient Boosted Trees (GBT) is a generalized boosting algorithm introduced by
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Jerome Friedman: http://www.salfordsystems.com/doc/GreedyFuncApproxSS.pdf .
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In contrast to the AdaBoost.M1 algorithm, GBT can deal with both multiclass
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classification and regression problems. Moreover, it can use any
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differential loss function, some popular ones are implemented.
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Decision trees (:ocv:class:`CvDTree`) usage as base learners allows to process ordered
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and categorical variables.
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Training the GBT model
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----------------------
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Gradient Boosted Trees model represents an ensemble of single regression trees
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built in a greedy fashion. Training procedure is an iterative proccess
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similar to the numerical optimization via the gradient descent method. Summary loss
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on the training set depends only on the current model predictions for the
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thaining samples, in other words
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:math:`\sum^N_{i=1}L(y_i, F(x_i)) \equiv \mathcal{L}(F(x_1), F(x_2), ... , F(x_N))
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\equiv \mathcal{L}(F)`. And the :math:`\mathcal{L}(F)`
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gradient can be computed as follows:
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.. math::
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grad(\mathcal{L}(F)) = \left( \dfrac{\partial{L(y_1, F(x_1))}}{\partial{F(x_1)}},
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\dfrac{\partial{L(y_2, F(x_2))}}{\partial{F(x_2)}}, ... ,
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\dfrac{\partial{L(y_N, F(x_N))}}{\partial{F(x_N)}} \right) .
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At every training step, a single regression tree is built to predict an
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antigradient vector components. Step length is computed corresponding to the
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loss function and separately for every region determined by the tree leaf. It
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can be eliminated by changing values of the leaves directly.
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See below the main scheme of the training proccess:
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#.
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Find the best constant model.
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#.
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For :math:`i` in :math:`[1,M]`:
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#.
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Compute the antigradient.
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#.
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Grow a regression tree to predict antigradient components.
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#.
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Change values in the tree leaves.
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#.
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Add the tree to the model.
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The following loss functions are implemented for regression problems:
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*
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Squared loss (``CvGBTrees::SQUARED_LOSS``):
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:math:`L(y,f(x))=\dfrac{1}{2}(y-f(x))^2`
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*
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Absolute loss (``CvGBTrees::ABSOLUTE_LOSS``):
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:math:`L(y,f(x))=|y-f(x)|`
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*
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Huber loss (``CvGBTrees::HUBER_LOSS``):
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:math:`L(y,f(x)) = \left\{ \begin{array}{lr}
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\delta\cdot\left(|y-f(x)|-\dfrac{\delta}{2}\right) & : |y-f(x)|>\delta\\
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\dfrac{1}{2}\cdot(y-f(x))^2 & : |y-f(x)|\leq\delta \end{array} \right.`,
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where :math:`\delta` is the :math:`\alpha`-quantile estimation of the
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:math:`|y-f(x)|`. In the current implementation :math:`\alpha=0.2`.
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The following loss functions are implemented for classification problems:
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*
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Deviance or cross-entropy loss (``CvGBTrees::DEVIANCE_LOSS``):
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:math:`K` functions are built, one function for each output class, and
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:math:`L(y,f_1(x),...,f_K(x)) = -\sum^K_{k=0}1(y=k)\ln{p_k(x)}`,
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where :math:`p_k(x)=\dfrac{\exp{f_k(x)}}{\sum^K_{i=1}\exp{f_i(x)}}`
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is the estimation of the probability of :math:`y=k`.
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As a result, you get the following model:
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.. math:: f(x) = f_0 + \nu\cdot\sum^M_{i=1}T_i(x) ,
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where :math:`f_0` is an initial guess (the best constant model) and :math:`\nu`
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is a regularization parameter from the interval :math:`(0,1]`, futher called
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*shrinkage*.
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Predicting with the GBT Model
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-------------------------
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To get the GBT model prediciton, you need to compute the sum of responses of
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all the trees in the ensemble. For regression problems, it is the answer.
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For classification problems, the result is :math:`\arg\max_{i=1..K}(f_i(x))`.
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.. highlight:: cpp
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CvGBTreesParams
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---------------
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.. ocv:class:: CvGBTreesParams
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GBT training parameters.
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The structure contains parameters for each sigle decision tree in the ensemble,
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as well as the whole model characteristics. The structure is derived from
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:ocv:class:`CvDTreeParams` but not all of the decision tree parameters are supported:
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cross-validation, pruning, and class priorities are not used.
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CvGBTreesParams::CvGBTreesParams
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--------------------------------
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.. ocv:function:: CvGBTreesParams::CvGBTreesParams()
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.. ocv:function:: CvGBTreesParams::CvGBTreesParams( int loss_function_type, int weak_count, float shrinkage, float subsample_portion, int max_depth, bool use_surrogates )
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:param loss_function_type: Type of the loss function used for training
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(see :ref:`Training the GBT model`). It must be one of the
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following types: ``CvGBTrees::SQUARED_LOSS``, ``CvGBTrees::ABSOLUTE_LOSS``,
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``CvGBTrees::HUBER_LOSS``, ``CvGBTrees::DEVIANCE_LOSS``. The first three
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types are used for regression problems, and the last one for
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classification.
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:param weak_count: Count of boosting algorithm iterations. ``weak_count*K`` is the total
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count of trees in the GBT model, where ``K`` is the output classes count
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(equal to one in case of a regression).
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:param shrinkage: Regularization parameter (see :ref:`Training the GBT model`).
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:param subsample_portion: Portion of the whole training set used for each algorithm iteration.
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Subset is generated randomly. For more information see
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http://www.salfordsystems.com/doc/StochasticBoostingSS.pdf.
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:param max_depth: Maximal depth of each decision tree in the ensemble (see :ocv:class:`CvDTree`).
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:param use_surrogates: If ``true``, surrogate splits are built (see :ocv:class:`CvDTree`).
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By default the following constructor is used:
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.. code-block:: cpp
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CvGBTreesParams(CvGBTrees::SQUARED_LOSS, 200, 0.8f, 0.01f, 3, false)
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: CvDTreeParams( 3, 10, 0, false, 10, 0, false, false, 0 )
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CvGBTrees
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---------
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.. ocv:class:: CvGBTrees
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The class implements the Gradient boosted tree model as described in the beginning of this section.
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CvGBTrees::CvGBTrees
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--------------------
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Default and training constructors.
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.. ocv:function:: CvGBTrees::CvGBTrees()
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.. ocv:function:: CvGBTrees::CvGBTrees( const Mat& trainData, int tflag, const Mat& responses, const Mat& varIdx=Mat(), const Mat& sampleIdx=Mat(), const Mat& varType=Mat(), const Mat& missingDataMask=Mat(), CvGBTreesParams params=CvGBTreesParams() )
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.. ocv:function::CvGBTrees::CvGBTrees( const CvMat* trainData, int tflag, const CvMat* responses, const CvMat* varIdx=0, const CvMat* sampleIdx=0, const CvMat* varType=0, const CvMat* missingDataMask=0, CvGBTreesParams params=CvGBTreesParams() )
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.. ocv:pyfunction:: cv2.GBTrees([trainData, tflag, responses[, varIdx[, sampleIdx[, varType[, missingDataMask[, params]]]]]]) -> <GBTrees object>
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The constructors follow conventions of :ocv:func:`CvStatModel::CvStatModel`. See :ocv:func:`CvStatModel::train` for parameters descriptions.
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CvGBTrees::train
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----------------
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Trains a Gradient boosted tree model.
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.. ocv:function:: bool CvGBTrees::train(const Mat& trainData, int tflag, const Mat& responses, const Mat& varIdx=Mat(), const Mat& sampleIdx=Mat(), const Mat& varType=Mat(), const Mat& missingDataMask=Mat(), CvGBTreesParams params=CvGBTreesParams(), bool update=false)
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.. ocv:function::bool CvGBTrees::train( const CvMat* trainData, int tflag, const CvMat* responses, const CvMat* varIdx=0, const CvMat* sampleIdx=0, const CvMat* varType=0, const CvMat* missingDataMask=0, CvGBTreesParams params=CvGBTreesParams(), bool update=false )
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.. ocv:function::bool CvGBTrees::train(CvMLData* data, CvGBTreesParams params=CvGBTreesParams(), bool update=false)
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.. ocv:pyfunction:: cv2.GBTrees.train(trainData, tflag, responses[, varIdx[, sampleIdx[, varType[, missingDataMask[, params[, update]]]]]]) -> retval
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The first train method follows the common template (see :ocv:func:`CvStatModel::train`).
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Both ``tflag`` values (``CV_ROW_SAMPLE``, ``CV_COL_SAMPLE``) are supported.
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``trainData`` must be of the ``CV_32F`` type. ``responses`` must be a matrix of type
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``CV_32S`` or ``CV_32F``. In both cases it is converted into the ``CV_32F``
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matrix inside the training procedure. ``varIdx`` and ``sampleIdx`` must be a
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list of indices (``CV_32S``) or a mask (``CV_8U`` or ``CV_8S``). ``update`` is
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a dummy parameter.
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The second form of :ocv:func:`CvGBTrees::train` function uses :ocv:class:`CvMLData` as a
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data set container. ``update`` is still a dummy parameter.
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All parameters specific to the GBT model are passed into the training function
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as a :ocv:class:`CvGBTreesParams` structure.
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CvGBTrees::predict
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------------------
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Predicts a response for an input sample.
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.. ocv:function:: float CvGBTrees::predict(const Mat& sample, const Mat& missing=Mat(), const Range& slice = Range::all(), int k=-1) const
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.. ocv:function::float CvGBTrees::predict( const CvMat* sample, const CvMat* missing=0, CvMat* weakResponses=0, CvSlice slice = CV_WHOLE_SEQ, int k=-1 ) const
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.. ocv:pyfunction:: cv2.GBTrees.predict(sample[, missing[, slice[, k]]]) -> retval
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:param sample: Input feature vector that has the same format as every training set
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element. If not all the variables were actualy used during training,
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``sample`` contains forged values at the appropriate places.
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:param missing: Missing values mask, which is a dimentional matrix of the same size as
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``sample`` having the ``CV_8U`` type. ``1`` corresponds to the missing value
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in the same position in the ``sample`` vector. If there are no missing values
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in the feature vector, an empty matrix can be passed instead of the missing mask.
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:param weak_responses: Matrix used to obtain predictions of all the trees.
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The matrix has :math:`K` rows,
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where :math:`K` is the count of output classes (1 for the regression case).
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The matrix has as many columns as the ``slice`` length.
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:param slice: Parameter defining the part of the ensemble used for prediction.
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If ``slice = Range::all()``, all trees are used. Use this parameter to
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get predictions of the GBT models with different ensemble sizes learning
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only one model.
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:param k: Number of tree ensembles built in case of the classification problem
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(see :ref:`Training the GBT model`). Use this
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parameter to change the ouput to sum of the trees' predictions in the
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``k``-th ensemble only. To get the total GBT model prediction, ``k`` value
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must be -1. For regression problems, ``k`` is also equal to -1.
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The method predicts the response corresponding to the given sample
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(see :ref:`Predicting with the GBT model`).
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The result is either the class label or the estimated function value. The
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:ocv:func:`predict` method enables using the parallel version of the GBT model
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prediction if the OpenCV is built with the TBB library. In this case, predictions
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of single trees are computed in a parallel fashion.
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CvGBTrees::clear
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----------------
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Clears the model.
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.. ocv:function:: void CvGBTrees::clear()
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.. ocv:pyfunction:: cv2.GBTrees.clear() -> None
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The function deletes the data set information and all the weak models and sets all internal
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variables to the initial state. The function is called in :ocv:func:`CvGBTrees::train` and in the
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destructor.
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CvGBTrees::calc_error
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---------------------
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Calculates a training or testing error.
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.. ocv:function:: float CvGBTrees::calc_error( CvMLData* _data, int type, std::vector<float> *resp = 0 )
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:param _data: Data set.
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:param type: Parameter defining the error that should be computed: train (``CV_TRAIN_ERROR``) or test
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(``CV_TEST_ERROR``).
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:param resp: If non-zero, a vector of predictions on the corresponding data set is
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returned.
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If the :ocv:class:`CvMLData` data is used to store the data set, :ocv:func:`calc_error` can be
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used to get a training/testing error easily and (optionally) all predictions
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on the training/testing set. If the Intel* TBB* library is used, the error is computed in a
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parallel way, namely, predictions for different samples are computed at the same time.
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In case of a regression problem, a mean squared error is returned. For
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classifications, the result is a misclassification error in percent.
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