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SHOGUN
4.1.0
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SHOGUN
4.1.0
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This class implements the Classification And Regression Trees algorithm by Breiman et al for decision tree learning. A CART tree is a binary decision tree that is constructed by splitting a node into two child nodes repeatedly, beginning with the root node that contains the whole dataset.
TREE GROWING PROCESS :
During the tree growing process, we recursively split a node into left child and right child so that the resulting nodes are "purest". We do this until any of the stopping criteria is met. To find the best split, we scan through all possible splits in all predictive attributes. The best split is one that maximises some splitting criterion. For classification tasks, ie. when the dependent attribute is categorical, the Gini index is used. For regression tasks, ie. when the dependent variable is continuous, least squares deviation is used. The algorithm uses two stopping criteria : if node becomes completely "pure", ie. all its members have identical dependent variable, or all of them have identical predictive attributes (independent variables).
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COST-COMPLEXITY PRUNING :
The maximal tree, \(T_max\) grown during tree growing process is bound to overfit. Hence pruning becomes necessary. Cost-Complexity pruning yields a list of subtrees of varying depths using the complexity normalized resubstitution error, \(R_\alpha(T)\). The resubstitution error R(T) is a measure of how well a decision tree fits the training data. This measure favours larger trees over smaller ones. However, complexity normalized resubstitution error, adds penalty for increased complexity and hence counters overfitting.
\(R_\alpha(T)=R(T)+\alpha \times (numleaves)\)
The best subtree among the list of subtrees can be chosen using cross validation or using best-fit in the test dataset.
cf. https://onlinecourses.science.psu.edu/stat557/node/93
HANDLING MISSING VALUES :
While choosing the best split at a node, missing attribute values are left out. But data vectors with missing values of the best attribute chosen are sent to left child or right child using a surrogate split. A surrogate split is one that imitates the best split as closely as possible. While choosing a surrogate split, all splits alternative to the best split are scaned and the degree of closeness between the two is measured using a metric called predictive measure of association, \(\lambda_{i,j}\).
\(\lambda_{i,j} = \frac{min(P_L,P_R)-(1-P_{L_iL_j}-P_{R_iR_j})}{min(P_L,P_R)}\)
where \(P_L\) and \(P_R\) are the node probabilities for the optimal split of node i into left and right nodes respectively, \(P_{L_iL_j}\) ( \(P_{R_iR_j}\) resp.) is the probability that both (optimal) node i and (surrogate) node j send an observation to the Left (Right resp.).
We use best surrogate split, 2nd best surrogate split and so on until all data points with missing attributes in a node have been sent to left/right child. If all possible surrogate splits are used up but some data points are still to be assigned left/right child, majority rule is used, ie. the data points are assigned the child where majority of data points have gone from the node.
cf. http://pic.dhe.ibm.com/infocenter/spssstat/v20r0m0/index.jsp?topic=%2Fcom.ibm.spss.statistics.help%2Falg_tree-cart.htm
Public Types | |
| typedef CTreeMachineNode < CARTreeNodeData > | node_t |
| typedef CBinaryTreeMachineNode < CARTreeNodeData > | bnode_t |
Public Attributes | |
| SGIO * | io |
| Parallel * | parallel |
| Version * | version |
| Parameter * | m_parameters |
| Parameter * | m_model_selection_parameters |
| Parameter * | m_gradient_parameters |
| uint32_t | m_hash |
Static Public Attributes | |
| static const float64_t | MISSING =CMath::MAX_REAL_NUMBER |
| static const float64_t | MIN_SPLIT_GAIN =1e-7 |
| static const float64_t | EQ_DELTA =1e-7 |
Protected Attributes | |
| float64_t | m_label_epsilon |
| SGVector< bool > | m_nominal |
| SGVector< float64_t > | m_weights |
| bool | m_types_set |
| bool | m_weights_set |
| bool | m_apply_cv_pruning |
| int32_t | m_folds |
| EProblemType | m_mode |
| CDynamicArray< float64_t > * | m_alphas |
| int32_t | m_max_depth |
| int32_t | m_min_node_size |
| CTreeMachineNode < CARTreeNodeData > * | m_root |
| CDynamicObjectArray * | m_machines |
| float64_t | m_max_train_time |
| CLabels * | m_labels |
| ESolverType | m_solver_type |
| bool | m_store_model_features |
| bool | m_data_locked |
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bnode_t type- Tree node with max 2 possible children
Definition at line 55 of file TreeMachine.h.
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node_t type- Tree node with many possible children
Definition at line 52 of file TreeMachine.h.
| CCARTree | ( | ) |
default constructor
Definition at line 40 of file CARTree.cpp.
| CCARTree | ( | SGVector< bool > | attribute_types, |
| EProblemType | prob_type = PT_MULTICLASS |
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constructor
| attribute_types | type of each predictive attribute (true for nominal, false for ordinal/continuous) |
| prob_type | machine problem type - PT_MULTICLASS or PT_REGRESSION |
Definition at line 46 of file CARTree.cpp.
| CCARTree | ( | SGVector< bool > | attribute_types, |
| EProblemType | prob_type, | ||
| int32_t | num_folds, | ||
| bool | cv_prune | ||
| ) |
constructor - to be used while using cross-validation pruning
| attribute_types | type of each predictive attribute (true for nominal, false for ordinal/continuous) |
| prob_type | machine problem type - PT_MULTICLASS or PT_REGRESSION |
| num_folds | number of subsets used in cross-valiation |
| cv_prune | - whether to use cross-validation pruning |
Definition at line 54 of file CARTree.cpp.
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virtual |
destructor
Definition at line 65 of file CARTree.cpp.
apply machine to data if data is not specified apply to the current features
| data | (test)data to be classified |
Definition at line 152 of file Machine.cpp.
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virtualinherited |
apply machine to data in means of binary classification problem
Reimplemented in CKernelMachine, COnlineLinearMachine, CWDSVMOcas, CNeuralNetwork, CLinearMachine, CGaussianProcessClassification, CDomainAdaptationSVMLinear, CDomainAdaptationSVM, CPluginEstimate, and CBaggingMachine.
Definition at line 208 of file Machine.cpp.
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uses current subtree to classify/regress data
| feats | data to be classified/regressed |
| current | root of current subtree |
Definition at line 976 of file CARTree.cpp.
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apply machine to data in means of latent problem
Reimplemented in CLinearLatentMachine.
Definition at line 232 of file Machine.cpp.
Applies a locked machine on a set of indices. Error if machine is not locked
| indices | index vector (of locked features) that is predicted |
Definition at line 187 of file Machine.cpp.
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applies a locked machine on a set of indices for binary problems
Reimplemented in CKernelMachine, and CMultitaskLinearMachine.
Definition at line 238 of file Machine.cpp.
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applies a locked machine on a set of indices for latent problems
Definition at line 266 of file Machine.cpp.
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applies a locked machine on a set of indices for multiclass problems
Definition at line 252 of file Machine.cpp.
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applies a locked machine on a set of indices for regression problems
Reimplemented in CKernelMachine.
Definition at line 245 of file Machine.cpp.
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applies a locked machine on a set of indices for structured problems
Definition at line 259 of file Machine.cpp.
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classify data using Classification Tree
| data | data to be classified |
Reimplemented from CMachine.
Definition at line 99 of file CARTree.cpp.
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applies to one vector
Reimplemented in CKernelMachine, CRelaxedTree, CWDSVMOcas, COnlineLinearMachine, CLinearMachine, CMultitaskLinearMachine, CMulticlassMachine, CKNN, CDistanceMachine, CMultitaskLogisticRegression, CMultitaskLeastSquaresRegression, CScatterSVM, CGaussianNaiveBayes, CPluginEstimate, and CFeatureBlockLogisticRegression.
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Get regression labels using Regression Tree
| data | data whose regression output is needed |
Reimplemented from CMachine.
Definition at line 111 of file CARTree.cpp.
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apply machine to data in means of SO classification problem
Reimplemented in CLinearStructuredOutputMachine.
Definition at line 226 of file Machine.cpp.
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Builds a dictionary of all parameters in SGObject as well of those of SGObjects that are parameters of this object. Dictionary maps parameters to the objects that own them.
| dict | dictionary of parameters to be built. |
Definition at line 597 of file SGObject.cpp.
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CARTtrain - recursive CART training method
| data | training data |
| weights | vector of weights of data points |
| labels | labels of data points |
| level | current tree depth |
Definition at line 285 of file CARTree.cpp.
| void clear_feature_types | ( | ) |
clear feature types of various features
Definition at line 197 of file CARTree.cpp.
| void clear_weights | ( | ) |
clear weights of data points
Definition at line 180 of file CARTree.cpp.
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Creates a clone of the current object. This is done via recursively traversing all parameters, which corresponds to a deep copy. Calling equals on the cloned object always returns true although none of the memory of both objects overlaps.
Definition at line 714 of file SGObject.cpp.
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computes best attribute for CARTtrain
| mat | data matrix |
| weights | data weights |
| labels_vec | data labels |
| left | stores feature values for left transition |
| right | stores feature values for right transition |
| is_left_final | stores which feature vectors go to the left child |
| num_missing | number of missing attributes |
| count_left | stores number of feature values for left transition |
| count_right | stores number of feature values for right transition |
Reimplemented in CRandomCARTree.
Definition at line 486 of file CARTree.cpp.
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computes error in classification/regression for classification it eveluates weight_missclassified/total_weight for regression it evaluates weighted sum of squared error/total_weight
| labels | the labels whose error needs to be calculated |
| reference | actual labels against which test labels are compared |
| weights | weights associated with the labels |
Definition at line 1198 of file CARTree.cpp.
recursively cuts weakest link(s) in a tree
| node | the root of subtree whose weakest link it cuts |
| alpha | alpha value corresponding to weakest link |
Definition at line 1305 of file CARTree.cpp.
Locks the machine on given labels and data. After this call, only train_locked and apply_locked may be called
Only possible if supports_locking() returns true
| labs | labels used for locking |
| features | features used for locking |
Reimplemented in CKernelMachine.
Definition at line 112 of file Machine.cpp.
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Unlocks a locked machine and restores previous state
Reimplemented in CKernelMachine.
Definition at line 143 of file Machine.cpp.
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A deep copy. All the instance variables will also be copied.
Definition at line 198 of file SGObject.cpp.
Recursively compares the current SGObject to another one. Compares all registered numerical parameters, recursion upon complex (SGObject) parameters. Does not compare pointers!
May be overwritten but please do with care! Should not be necessary in most cases.
| other | object to compare with |
| accuracy | accuracy to use for comparison (optional) |
| tolerant | allows linient check on float equality (within accuracy) |
Definition at line 618 of file SGObject.cpp.
recursively finds alpha corresponding to weakest link(s)
| node | the root of subtree whose weakest link it finds |
Definition at line 1284 of file CARTree.cpp.
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recursively forms base case $ft_1$f tree from $ft_max$f during pruning
| node | the root of current subtree |
Definition at line 1335 of file CARTree.cpp.
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returns gain in regression case
| wleft | left child weight distribution |
| wright | right child weights distribution |
| wtotal | weight distribution in current node |
| labels | regression labels |
Definition at line 918 of file CARTree.cpp.
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returns gain in Gini impurity measure
| wleft | left child label distribution |
| wright | right child label distribution |
| wtotal | label distribution in current node |
Definition at line 932 of file CARTree.cpp.
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get classifier type
Reimplemented in CLaRank, CSVMLight, CDualLibQPBMSOSVM, CNeuralNetwork, CCCSOSVM, CLeastAngleRegression, CLDA, CKernelRidgeRegression, CLibLinearMTL, CBaggingMachine, CLibLinear, CGaussianProcessClassification, CKMeans, CLibSVR, CQDA, CGaussianNaiveBayes, CSVRLight, CMCLDA, CLinearRidgeRegression, CKNN, CScatterSVM, CGaussianProcessRegression, CSGDQN, CSVMSGD, CSVMOcas, COnlineSVMSGD, CLeastSquaresRegression, CMKLRegression, CDomainAdaptationSVMLinear, CMKLMulticlass, CWDSVMOcas, CHierarchical, CMKLOneClass, CLibSVM, CStochasticSOSVM, CMKLClassification, CDomainAdaptationSVM, CLPBoost, CPerceptron, CAveragedPerceptron, CFWSOSVM, CNewtonSVM, CLPM, CGMNPSVM, CSVMLightOneClass, CSVMLin, CMulticlassLibSVM, CLibSVMOneClass, CMPDSVM, CGPBTSVM, CGNPPSVM, and CCPLEXSVM.
Definition at line 92 of file Machine.cpp.
| SGVector< bool > get_feature_types | ( | ) | const |
set feature types of various features
Definition at line 192 of file CARTree.cpp.
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| float64_t get_label_epsilon | ( | ) |
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get problem type - multiclass classification or regression
Reimplemented from CBaseMulticlassMachine.
| int32_t get_max_depth | ( | ) | const |
get max allowed tree depth
Definition at line 214 of file CARTree.cpp.
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| int32_t get_min_node_size | ( | ) | const |
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Definition at line 498 of file SGObject.cpp.
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Returns description of a given parameter string, if it exists. SG_ERROR otherwise
| param_name | name of the parameter |
Definition at line 522 of file SGObject.cpp.
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Returns index of model selection parameter with provided index
| param_name | name of model selection parameter |
Definition at line 535 of file SGObject.cpp.
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get name
Reimplemented from CTreeMachine< CARTreeNodeData >.
Reimplemented in CRandomCARTree.
| int32_t get_num_folds | ( | ) | const |
get number of subsets used for cross validation
Definition at line 203 of file CARTree.cpp.
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get number of machines
Definition at line 27 of file BaseMulticlassMachine.cpp.
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modify labels for compute_best_attribute
| labels_vec | labels vector |
| n_ulabels | stores number of unique labels |
Definition at line 462 of file CARTree.cpp.
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returns Gini impurity of a node
| weighted_lab_classes | vector of weights associated with various labels |
| total_weight | stores the total weight of all classes |
Definition at line 944 of file CARTree.cpp.
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handles missing values for a chosen continuous surrogate attribute
| m | training data matrix |
| missing_vecs | column indices of vectors with missing attribute in data matrix |
| association_index | stores the final lambda values used to address members of missing_vecs |
| intersect_vecs | column indices of vectors with known values for the best attribute as well as the chosen surrogate |
| is_left | whether a vector goes into left child |
| weights | weights of training data vectors |
| p | min(p_l,p_r) in the lambda formula |
| attr | surrogate attribute chosen for split |
Definition at line 781 of file CARTree.cpp.
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handles missing values for a chosen nominal surrogate attribute
| m | training data matrix |
| missing_vecs | column indices of vectors with missing attribute in data matrix |
| association_index | stores the final lambda values used to address members of missing_vecs |
| intersect_vecs | column indices of vectors with known values for the best attribute as well as the chosen surrogate |
| is_left | whether a vector goes into left child |
| weights | weights of training data vectors |
| p | min(p_l,p_r) in the lambda formula |
| attr | surrogate attribute chosen for split |
Definition at line 838 of file CARTree.cpp.
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initializes members of class
Definition at line 1361 of file CARTree.cpp.
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If the SGSerializable is a class template then TRUE will be returned and GENERIC is set to the type of the generic.
| generic | set to the type of the generic if returning TRUE |
Definition at line 296 of file SGObject.cpp.
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whether labels supplied are valid for current problem type
| lab | labels supplied |
Reimplemented from CBaseMulticlassMachine.
Definition at line 89 of file CARTree.cpp.
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returns least squares deviation
| labels | regression labels |
| weights | weights of regression data points |
| total_weight | stores sum of weights in weights vector |
Definition at line 958 of file CARTree.cpp.
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Load this object from file. If it will fail (returning FALSE) then this object will contain inconsistent data and should not be used!
| file | where to load from |
| prefix | prefix for members |
Definition at line 369 of file SGObject.cpp.
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Can (optionally) be overridden to post-initialize some member variables which are not PARAMETER::ADD'ed. Make sure that at first the overridden method BASE_CLASS::LOAD_SERIALIZABLE_POST is called.
| ShogunException | will be thrown if an error occurs. |
Reimplemented in CKernel, CWeightedDegreePositionStringKernel, CList, CAlphabet, CLinearHMM, CGaussianKernel, CInverseMultiQuadricKernel, CCircularKernel, and CExponentialKernel.
Definition at line 426 of file SGObject.cpp.
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Can (optionally) be overridden to pre-initialize some member variables which are not PARAMETER::ADD'ed. Make sure that at first the overridden method BASE_CLASS::LOAD_SERIALIZABLE_PRE is called.
| ShogunException | will be thrown if an error occurs. |
Reimplemented in CDynamicArray< T >, CDynamicArray< float64_t >, CDynamicArray< float32_t >, CDynamicArray< int32_t >, CDynamicArray< char >, CDynamicArray< bool >, and CDynamicObjectArray.
Definition at line 421 of file SGObject.cpp.
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Definition at line 262 of file SGObject.cpp.
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prints all parameter registered for model selection and their type
Definition at line 474 of file SGObject.cpp.
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prints registered parameters out
| prefix | prefix for members |
Definition at line 308 of file SGObject.cpp.
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prune by cross validation
| data | training data |
| folds | the integer V for V-fold cross validation |
Definition at line 1059 of file CARTree.cpp.
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cost-complexity pruning
| tree | the tree to be pruned |
Definition at line 1236 of file CARTree.cpp.
| void prune_using_test_dataset | ( | CDenseFeatures< float64_t > * | feats, |
| CLabels * | gnd_truth, | ||
| SGVector< float64_t > | weights = SGVector<float64_t>() |
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uses test dataset to choose best pruned subtree
| feats | test data to be used |
| gnd_truth | test labels |
| weights | weights of data points |
Definition at line 123 of file CARTree.cpp.
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Save this object to file.
| file | where to save the object; will be closed during returning if PREFIX is an empty string. |
| prefix | prefix for members |
Definition at line 314 of file SGObject.cpp.
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Can (optionally) be overridden to post-initialize some member variables which are not PARAMETER::ADD'ed. Make sure that at first the overridden method BASE_CLASS::SAVE_SERIALIZABLE_POST is called.
| ShogunException | will be thrown if an error occurs. |
Reimplemented in CKernel.
Definition at line 436 of file SGObject.cpp.
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Can (optionally) be overridden to pre-initialize some member variables which are not PARAMETER::ADD'ed. Make sure that at first the overridden method BASE_CLASS::SAVE_SERIALIZABLE_PRE is called.
| ShogunException | will be thrown if an error occurs. |
Reimplemented in CKernel, CDynamicArray< T >, CDynamicArray< float64_t >, CDynamicArray< float32_t >, CDynamicArray< int32_t >, CDynamicArray< char >, CDynamicArray< bool >, and CDynamicObjectArray.
Definition at line 431 of file SGObject.cpp.
| void set_feature_types | ( | SGVector< bool > | ft | ) |
set feature types of various features
| ft | bool vector true for nominal feature false for continuous feature type |
Definition at line 186 of file CARTree.cpp.
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Definition at line 41 of file SGObject.cpp.
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Definition at line 46 of file SGObject.cpp.
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Definition at line 51 of file SGObject.cpp.
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Definition at line 56 of file SGObject.cpp.
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Definition at line 61 of file SGObject.cpp.
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Definition at line 66 of file SGObject.cpp.
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Definition at line 71 of file SGObject.cpp.
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Definition at line 76 of file SGObject.cpp.
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Definition at line 81 of file SGObject.cpp.
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Definition at line 86 of file SGObject.cpp.
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Definition at line 91 of file SGObject.cpp.
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Definition at line 96 of file SGObject.cpp.
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Definition at line 101 of file SGObject.cpp.
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Definition at line 106 of file SGObject.cpp.
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Definition at line 111 of file SGObject.cpp.
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set generic type to T
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set the parallel object
| parallel | parallel object to use |
Definition at line 241 of file SGObject.cpp.
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set the version object
| version | version object to use |
Definition at line 283 of file SGObject.cpp.
| void set_label_epsilon | ( | float64_t | epsilon | ) |
set label epsilon
| epsilon | equality range for regression labels |
Definition at line 236 of file CARTree.cpp.
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set labels - automagically switch machine problem type based on type of labels supplied
| lab | labels |
Reimplemented from CMachine.
Definition at line 70 of file CARTree.cpp.
| void set_machine_problem_type | ( | EProblemType | mode | ) |
set problem type - multiclass classification or regression
| mode | EProblemType PT_MULTICLASS or PT_REGRESSION |
Definition at line 84 of file CARTree.cpp.
| void set_max_depth | ( | int32_t | depth | ) |
set max allowed tree depth
| depth | max allowed tree depth |
Definition at line 219 of file CARTree.cpp.
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set maximum training time
| t | maximimum training time |
Definition at line 82 of file Machine.cpp.
| void set_min_node_size | ( | int32_t | nsize | ) |
set min allowed node size
| nsize | min allowed node size |
Definition at line 230 of file CARTree.cpp.
| void set_num_folds | ( | int32_t | folds | ) |
set number of subsets for cross validation
| folds | number of folds used in cross validation |
Definition at line 208 of file CARTree.cpp.
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Setter for store-model-features-after-training flag
| store_model | whether model should be stored after training |
Definition at line 107 of file Machine.cpp.
set weights of data points
| w | vector of weights |
Definition at line 169 of file CARTree.cpp.
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A shallow copy. All the SGObject instance variables will be simply assigned and SG_REF-ed.
Reimplemented in CGaussianKernel.
Definition at line 192 of file SGObject.cpp.
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enable unlocked cross-validation - no model features to store
Reimplemented from CMachine.
Definition at line 152 of file TreeMachine.h.
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Reimplemented in CKernelMachine, and CMultitaskLinearMachine.
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handles missing values through surrogate splits
| data | training data matrix |
| weights | vector of weights of data points |
| nm_left | whether a data point is put into left child (available for only data points with non-missing attribute attr) |
| attr | best attribute chosen for split |
Definition at line 706 of file CARTree.cpp.
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train machine
| data | training data (parameter can be avoided if distance or kernel-based classifiers are used and distance/kernels are initialized with train data). If flag is set, model features will be stored after training. |
Reimplemented in CRelaxedTree, CAutoencoder, CSGDQN, and COnlineSVMSGD.
Definition at line 39 of file Machine.cpp.
Trains a locked machine on a set of indices. Error if machine is not locked
NOT IMPLEMENTED
| indices | index vector (of locked features) that is used for training |
Reimplemented in CKernelMachine, and CMultitaskLinearMachine.
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train machine - build CART from training data
| data | training data |
Reimplemented from CMachine.
Definition at line 242 of file CARTree.cpp.
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returns whether machine require labels for training
Reimplemented in COnlineLinearMachine, CHierarchical, CLinearLatentMachine, CVwConditionalProbabilityTree, CConditionalProbabilityTree, and CLibSVMOneClass.
| void unset_cv_pruning | ( | ) |
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unset generic type
this has to be called in classes specializing a template class
Definition at line 303 of file SGObject.cpp.
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Updates the hash of current parameter combination
Definition at line 248 of file SGObject.cpp.
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io
Definition at line 369 of file SGObject.h.
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parameters wrt which we can compute gradients
Definition at line 384 of file SGObject.h.
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Hash of parameter values
Definition at line 387 of file SGObject.h.
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machines
Definition at line 56 of file BaseMulticlassMachine.h.
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model selection parameters
Definition at line 381 of file SGObject.h.
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parameters
Definition at line 378 of file SGObject.h.
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tree root
Definition at line 156 of file TreeMachine.h.
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parallel
Definition at line 372 of file SGObject.h.
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version
Definition at line 375 of file SGObject.h.