A Priori

class deslib.dcs.a_priori.APriori(pool_classifiers=None, k=7, DFP=False, with_IH=False, safe_k=None, IH_rate=0.3, selection_method='diff', diff_thresh=0.1, random_state=None, knn_classifier='knn', knn_metric='minkowski', knne=False, DSEL_perc=0.5, n_jobs=-1)

A Priori dynamic classifier selection.

The A Priori method uses the probability of correct classification of a given base classifier \(c_{i}\) for each neighbor \(x_{k}\) for the competence level estimation. Base classifiers with a higher probability of correct classification have a higher competence level. Moreover, the method also weights the influence of each neighbor \(x_{k}\) according to its Euclidean distance to the query sample. The closest neighbors have a higher influence on the competence level estimate.

A single classifier is selected only if its competence level is significantly higher than that of the other base classifiers in the pool (higher than a pre-defined threshold). Otherwise, all classifiers i the pool are combined using the majority voting rule.

Parameters:

pool_classifiers : list of classifiers (Default = None)

The generated_pool of classifiers trained for the corresponding classification problem. Each base classifiers should support the method “predict” and “predict_proba”. If None, then the pool of classifiers is a bagging classifier.

k : int (Default = 7)

Number of neighbors used to estimate the competence of the base classifiers.

DFP : Boolean (Default = False)

Determines if the dynamic frienemy pruning is applied.

with_IH : Boolean (Default = False)

Whether the hardness level of the region of competence is used to decide between using the DS algorithm or the KNN for classification of a given query sample.

safe_k : int (default = None)

The size of the indecision region.

IH_rate : float (default = 0.3)

Hardness threshold. If the hardness level of the competence region is lower than the IH_rate the KNN classifier is used. Otherwise, the DS

selection_method : String (Default = “best”)

Determines which method is used to select the base classifier after the competences are estimated.

diff_thresh : float (Default = 0.1)

Threshold to measure the difference between the competence level of the base classifiers for the random and diff selection schemes. If the difference is lower than the threshold, their performance are considered equivalent.

random_state : int, RandomState instance or None, optional (default=None)

If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by np.random.

knn_classifier : {‘knn’, ‘faiss’, None} (Default = ‘knn’)

The algorithm used to estimate the region of competence:

• ‘knn’ will use KNeighborsClassifier from sklearn

KNNE available on deslib.utils.knne

• ‘faiss’ will use Facebook’s Faiss similarity search through the class FaissKNNClassifier
• None, will use sklearn KNeighborsClassifier.

knn_metric : {‘minkowski’, ‘cosine’, ‘mahalanobis’} (Default = ‘minkowski’)

The metric used by the k-NN classifier to estimate distances.

• ‘minkowski’ will use minkowski distance.
• ‘cosine’ will use the cosine distance.
• ‘mahalanobis’ will use the mahalonibis distance.

knne : bool (Default=False)

Whether to use K-Nearest Neighbor Equality (KNNE) for the region of competence estimation.

DSEL_perc : float (Default = 0.5)

Percentage of the input data used to fit DSEL. Note: This parameter is only used if the pool of classifier is None or unfitted.

n_jobs : int, default=-1

The number of parallel jobs to run. None means 1 unless in a joblib.parallel_backend context. -1 means using all processors. Doesn’t affect fit method.

References

G. Giacinto and F. Roli, Methods for Dynamic Classifier Selection 10th Int. Conf. on Image Anal. and Proc., Venice, Italy (1999), 659-664.

Ko, Albert HR, Robert Sabourin, and Alceu Souza Britto Jr. “From dynamic classifier selection to dynamic ensemble selection.” Pattern Recognition 41.5 (2008): 1718-1731.

Britto, Alceu S., Robert Sabourin, and Luiz ES Oliveira. “Dynamic selection of classifiers—a comprehensive review.” Pattern Recognition 47.11 (2014): 3665-3680.

R. M. O. Cruz, R. Sabourin, and G. D. Cavalcanti, “Dynamic classifier selection: Recent advances and perspectives,” Information Fusion, vol. 41, pp. 195 – 216, 2018.

estimate_competence(competence_region, distances, predictions=None)

estimate the competence of each base classifier \(c_{i}\) for the classification of the query sample using the A Priori rule:

The competence level is estimated based on the probability of correct classification of the base classifier \(c_{i}\), considering all samples in the region of competence. This method also weights the influence of each training sample according to its Euclidean distance to the query instance. The closest samples have a higher influence in the computation of the competence level. The competence level estimate is represented by the following equation:

\[\delta_{i,j} = \frac{\sum_{k = 1}^{K}P(\omega_{l} \mid \mathbf{x}_{k} \in \omega_{l}, c_{i} )W_{k}}{\sum_{k = 1}^{K}W_{k}}\]

where \(\delta_{i,j}\) represents the competence level of \(c_{i}\) for the classification of query.

Parameters:

competence_region : array of shape (n_samples, n_neighbors)

Indices of the k nearest neighbors.

distances : array of shape (n_samples, n_neighbors)

Distances from the k nearest neighbors to the query.

predictions : array of shape (n_samples, n_classifiers)

Predictions of the base classifiers for the test examples.

Returns:

competences : array of shape (n_samples, n_classifiers)

Competence level estimated for each base classifier and test example.

fit(X, y)

Prepare the DS model by setting the KNN algorithm and pre-processing the information required to apply the DS method.

Parameters:

X : array of shape (n_samples, n_features)

Data used to fit the model.

y : array of shape (n_samples)

class labels of each example in X.

Returns:

self

predict(X)

Predict the class label for each sample in X.

Parameters:

X : array of shape (n_samples, n_features)

The input data.

Returns:

predicted_labels : array of shape (n_samples)

Predicted class label for each sample in X.

predict_proba(X)

Estimates the posterior probabilities for sample in X.

Parameters:

X : array of shape (n_samples, n_features)

The input data.

Returns:

predicted_proba : array of shape (n_samples, n_classes)

Probabilities estimates for each sample in X.

score(X, y, sample_weight=None)

Return the mean accuracy on the given test data and labels.

In multi-label classification, this is the subset accuracy which is a harsh metric since you require for each sample that each label set be correctly predicted.

Parameters:

X : array-like of shape (n_samples, n_features)

Test samples.

y : array-like of shape (n_samples,) or (n_samples, n_outputs)

True labels for X.

sample_weight : array-like of shape (n_samples,), default=None

Sample weights.

Returns:

score : float

Mean accuracy of self.predict(X) wrt. y.

select(competences)

Select the most competent classifier for the classification of the query sample given the competence level estimates. Four selection schemes are available.

Best : The base classifier with the highest competence level is selected. In cases where more than one base classifier achieves the same competence level, the one with the lowest index is selected. This method is the standard for the LCA, OLA, MLA techniques.

Diff : Select the base classifier that is significantly better than the others in the pool (when the difference between its competence level and the competence level of the other base classifiers is higher than a predefined threshold). If no base classifier is significantly better, the base classifier is selected randomly among the member with equivalent competence level.

Random : Selects a random base classifier among all base classifiers that achieved the same competence level.

ALL : all base classifiers with the max competence level estimates are selected (note that in this case the DCS technique becomes a DES technique).

Parameters:

competences : array of shape (n_samples, n_classifiers)

Competence level estimated for each base classifier and test example.

Returns:

selected_classifiers : array of shape [n_samples]

Indices of the selected base classifier for each sample. If the selection_method is set to ‘all’, a boolean matrix is returned, containing True for the selected base classifiers, otherwise false.