SVM#

This module uses a Support vector machine (SVM) with an RBF kernel to classify regions which are “safe” to explore in contrast to regions which are “unsafe” to explore since they are infinite. This is done in an attempt to hinder the exploration of parts of the parameter space which have a $-\infty$ log-posterior value. These values need to be filtered out since feeding them to the GP Regressor will break it. Nevertheless this is important information that we shouldn’t throw away. We will also need the SVM later when doing the MCMC run to tell the model which regions it shouldn’t visit. In essence our process shrinks the prior to a region where the model thinks that all values of the log-posterior distribution are finite.

class svm.SVM(C=10000000.0, kernel='rbf', degree=3, gamma='scale', coef0=0.0, shrinking=True, probability=False, tol=0.001, cache_size=200, class_weight=None, verbose=False, max_iter=-1, decision_function_shape='ovr', break_ties=False, random_state=None)[source]#

Bases: SVC

Wrapper for the sklearn RBF kernel SVM.

Classifies points as finite of non-finite, in order to exclude the latter from the training set of a parent GPR. It keeps track of the full training set, including classified-infinite points.

The classification is performed using a threshold understood as a positive difference against the current maximum y in the training set. The threshold is passed at fitting time and not at initialisation, in case the classifier is defined in a transformed coordinate space, with a transformation that changes through the training of the parent GPR. (NB: passing the threshold every time is a compromise that allows to keep the full training set stored in this object with non-reduced y values while avoiding preprocessing overhead.)

Also in case there is a coordinate transformation, the training set of this object should not be obtained directly, but via properties of the parent GP instead that will undo the transformation. The same applying to calling any method directly.

Parameters:

C (float, default=1e7) – Regularization parameter. The strength of the regularization is inversely proportional to C. Must be strictly positive. The penalty is a squared l2 penalty.
kernel ({'linear', 'poly', 'rbf', 'sigmoid', 'precomputed'}, default='rbf') – Specifies the kernel type to be used in the algorithm. It must be one of ‘linear’, ‘poly’, ‘rbf’, ‘sigmoid’, ‘precomputed’ or a callable. If none is given, ‘rbf’ will be used. If a callable is given it is used to pre-compute the kernel matrix from data matrices; that matrix should be an array of shape (n_samples, n_samples).
degree (int, default=3) – Degree of the polynomial kernel function (‘poly’). Ignored by all other kernels.
gamma ({'scale', 'auto'} or float, default='scale') –
Kernel coefficient for ‘rbf’, ‘poly’ and ‘sigmoid’.
- if gamma='scale' (default) is passed then it uses 1 / (n_features * X.var()) as value of gamma,
- if ‘auto’, uses 1 / n_features.
coef0 (float, default=0.0) – Independent term in kernel function. It is only significant in ‘poly’ and ‘sigmoid’.
shrinking (bool, default=True) – Whether to use the shrinking heuristic.
probability (bool, default=False) – Whether to enable probability estimates. This must be enabled prior to calling fit, will slow down that method as it internally uses 5-fold cross-validation, and predict_proba may be inconsistent with predict.
tol (float, default=1e-3) – Tolerance for stopping criterion.
cache_size (float, default=200) – Specify the size of the kernel cache (in MB).
class_weight (dict or 'balanced', default=None) – Set the parameter C of class i to class_weight[i]*C for SVC. If not given, all classes are supposed to have weight one. The “balanced” mode uses the values of y to automatically adjust weights inversely proportional to class frequencies in the input data as n_samples / (n_classes * np.bincount(y)).
verbose (bool, default=False) – Enable verbose output. Note that this setting takes advantage of a per-process runtime setting in libsvm that, if enabled, may not work properly in a multithreaded context.
max_iter (int, default=-1) – Hard limit on iterations within solver, or -1 for no limit.
decision_function_shape ({'ovo', 'ovr'}, default='ovr') – Whether to return a one-vs-rest (‘ovr’) decision function of shape (n_samples, n_classes) as all other classifiers, or the original one-vs-one (‘ovo’) decision function of libsvm which has shape (n_samples, n_classes * (n_classes - 1) / 2). However, one-vs-one (‘ovo’) is always used as multi-class strategy. The parameter is ignored for binary classification.
break_ties (bool, default=False) – If true, decision_function_shape='ovr', and number of classes > 2, predict will break ties according to the confidence values of decision_function; otherwise the first class among the tied classes is returned. Please note that breaking ties comes at a relatively high computational cost compared to a simple predict.
random_state (int, RandomState instance or None, default=None) – Controls the pseudo random number generation for shuffling the data for probability estimates. Ignored when probability is False. Pass an int for reproducible output across multiple function calls.

Attributes:

all_finite (bool) – Is true when all posterior values which have been sampled are finite which removes the need for fitting the SVM.
class_weight_ (ndarray of shape (n_classes,)) – Multipliers of parameter C for each class. Computed based on the class_weight parameter.
classes_ (ndarray of shape (n_classes,)) – The classes labels.
coef_ (ndarray of shape (n_classes * (n_classes - 1) / 2, n_features)) – Weights assigned to the features (coefficients in the primal problem). This is only available in the case of a linear kernel. coef_ is a readonly property derived from dual_coef_ and support_vectors_.
dual_coef_ (ndarray of shape (n_classes -1, n_SV)) – Dual coefficients of the support vector in the decision function, multiplied by their targets. For multiclass, coefficient for all 1-vs-1 classifiers. The layout of the coefficients in the multiclass case is somewhat non-trivial.
fit_status_ (int) – 0 if correctly fitted, 1 otherwise (will raise warning)
intercept_ (ndarray of shape (n_classes * (n_classes - 1) / 2,)) – Constants in decision function.
n_features_in_ (int) – Number of features seen during fit.
feature_names_in_ (ndarray of shape (n_features_in_,)) – Names of features seen during fit. Defined only when X has feature names that are all strings.
support_ (ndarray of shape (n_SV)) – Indices of support vectors.
support_vectors_ (ndarray of shape (n_SV, n_features)) – Support vectors.
n_support_ (ndarray of shape (n_classes,), dtype=int32) – Number of support vectors for each class.
probA_ (ndarray of shape (n_classes * (n_classes - 1) / 2))
probB_ (ndarray of shape (n_classes * (n_classes - 1) / 2)) – If probability=True, it corresponds to the parameters learned in Platt scaling to produce probability estimates from decision values. If probability=False, it’s an empty array. Platt scaling uses the logistic function 1 / (1 + exp(decision_value * probA_ + probB_)) where probA_ and probB_ are learned from the dataset..
shape_fit_ (tuple of int of shape (n_dimensions_of_X,)) – Array dimensions of training vector X.

property d#: Dimension of the feature space.

property abs_threshold#: Current absolute threshold for y values, in the transformed space of the SVM.

property n#: Number of training points.

fit(X, y, diff_threshold)[source]#

Fits the SVM with two categorial classes:

$\tilde{y}=True$ Finite points
$\tilde{y}=False$ Infinite points

where $\tilde{y}$ is produced after checking the input y’s against an internal threshold value, which may also be adjusted at this step.

Parameters:

X (array-like, shape = (n_samples, n_features)) – Training data.
y (array-like, shape = (n_samples, [n_output_dims])) – Target values.

Returns:

y_finite – Classification of current points.

Return type:

array-like bool

is_finite(y)[source]#

Returns the indices of the finite points, depending on the current threshold and maximum y value in the training set (not the input).

The y input must be passed in the space in which the SVM was defined.

predict(X, validate=True)[source]#

Wrapper for the predict method of the SVM which does the preprocessing. Returns a boolean array which is true at locations where the SVM predicts a finite posterior distribution and False where it predicts infinite values.

Parameters:

X (array-like, shape = (n_samples, n_features)) – Query points where SVM is evaluated.

Returns:

A boolean array which is True at locations predicted finite posterior
and False at locations with predicted infinite posterior.

Raises:

ValueError – “ndarray is not C-contiguous”: May be raised if validate is False. Call numpy.ascontiguousarray() on the input before the call.

set_fit_request(*, diff_threshold: bool | None | str = '$UNCHANGED$') → SVM#

Request metadata passed to the fit method.

Note that this method is only relevant if enable_metadata_routing=True (see sklearn.set_config()). Please see User Guide on how the routing mechanism works.

The options for each parameter are:

True: metadata is requested, and passed to fit if provided. The request is ignored if metadata is not provided.
False: metadata is not requested and the meta-estimator will not pass it to fit.
None: metadata is not requested, and the meta-estimator will raise an error if the user provides it.
str: metadata should be passed to the meta-estimator with this given alias instead of the original name.

The default (sklearn.utils.metadata_routing.UNCHANGED) retains the existing request. This allows you to change the request for some parameters and not others.

Added in version 1.3.

Note

This method is only relevant if this estimator is used as a sub-estimator of a meta-estimator, e.g. used inside a Pipeline. Otherwise it has no effect.

Parameters:: diff_threshold (str, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED) – Metadata routing for diff_threshold parameter in fit.
Returns:: self – The updated object.
Return type:: object

set_predict_request(*, validate: bool | None | str = '$UNCHANGED$') → SVM#

Request metadata passed to the predict method.

Note that this method is only relevant if enable_metadata_routing=True (see sklearn.set_config()). Please see User Guide on how the routing mechanism works.

The options for each parameter are:

True: metadata is requested, and passed to predict if provided. The request is ignored if metadata is not provided.
False: metadata is not requested and the meta-estimator will not pass it to predict.
None: metadata is not requested, and the meta-estimator will raise an error if the user provides it.
str: metadata should be passed to the meta-estimator with this given alias instead of the original name.

The default (sklearn.utils.metadata_routing.UNCHANGED) retains the existing request. This allows you to change the request for some parameters and not others.

Added in version 1.3.

Note

This method is only relevant if this estimator is used as a sub-estimator of a meta-estimator, e.g. used inside a Pipeline. Otherwise it has no effect.

Parameters:: validate (str, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED) – Metadata routing for validate parameter in predict.
Returns:: self – The updated object.
Return type:: object

set_score_request(*, sample_weight: bool | None | str = '$UNCHANGED$') → SVM#

Request metadata passed to the score method.

Note that this method is only relevant if enable_metadata_routing=True (see sklearn.set_config()). Please see User Guide on how the routing mechanism works.

The options for each parameter are:

True: metadata is requested, and passed to score if provided. The request is ignored if metadata is not provided.
False: metadata is not requested and the meta-estimator will not pass it to score.
None: metadata is not requested, and the meta-estimator will raise an error if the user provides it.
str: metadata should be passed to the meta-estimator with this given alias instead of the original name.

The default (sklearn.utils.metadata_routing.UNCHANGED) retains the existing request. This allows you to change the request for some parameters and not others.

Added in version 1.3.

Note

This method is only relevant if this estimator is used as a sub-estimator of a meta-estimator, e.g. used inside a Pipeline. Otherwise it has no effect.

Parameters:: sample_weight (str, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED) – Metadata routing for sample_weight parameter in score.
Returns:: self – The updated object.
Return type:: object

SVM

Contents

SVM#