Signature:
Bgolearn.fit(
    data_matrix,
    Measured_response,
    virtual_samples,
    Mission='Regression',
    Classifier='GaussianProcess',
    noise_std=None,
    Kriging_model=None,
    opt_num=1,
    min_search=True,
    CV_test=False,
    Dynamic_W=False,
    seed=42,
)

================================================================

:param data_matrix: data matrix of training dataset, X .

:param Measured_response: response of tarining dataset, y.

:param virtual_samples: designed virtual samples.

:param Mission: str, default 'Regression', the mission of optimization.  Mission = 'Regression' or 'Classification'

:param Classifier: if  Mission == 'Classification', classifier is used.
        if user isn't applied one, Bgolearn will call a pre-set classifier.
        default, Classifier = 'GaussianProcess', i.e., Gaussian Process Classifier.
        five different classifiers are pre-setd in Bgolearn:
        'GaussianProcess' --> Gaussian Process Classifier (default)
        'LogisticRegression' --> Logistic Regression
        'NaiveBayes' --> Naive Bayes Classifier
        'SVM' --> Support Vector Machine Classifier
        'RandomForest' --> Random Forest Classifier

:param noise_std: float or ndarray of shape (n_samples,), default=None
        Value added to the diagonal of the kernel matrix during fitting.
        This can prevent a potential numerical issue during fitting, by
        ensuring that the calculated values form a positive definite matrix.
        It can also be interpreted as the variance of additional Gaussian.
        measurement noise on the training observations.

        if noise_std is not None, a noise value will be estimated by maximum likelihood
        on training dataset.

:param Kriging_model (default None):
        str, Kriging_model = 'SVM', 'RF', 'AdaB', 'MLP'
        The  machine learning models will be implemented: Support Vector Machine (SVM), 
        Random Forest(RF), AdaBoost(AdaB), and Multi-Layer Perceptron (MLP).
        The estimation uncertainity will be determined by Boostsrap sampling.
    or  
        a user defined callable Kriging model, has an attribute of <fit_pre>
        if user isn't applied one, Bgolearn will call a pre-set Kriging model
        atribute <fit_pre> : 
        input -> xtrain, ytrain, xtest ; 
        output -> predicted  mean and std of xtest

        e.g. (take GaussianProcessRegressor in sklearn):
        class Kriging_model(object):
            def fit_pre(self,xtrain,ytrain,xtest):
                # instantiated model
                kernel = RBF()
                mdoel = GaussianProcessRegressor(kernel=kernel).fit(xtrain,ytrain)
                # defined the attribute's outputs
                mean,std = mdoel.predict(xtest,return_std=True)
                return mean,std    

        e.g. (MultiModels estimations):
        class Kriging_model(object):
            def fit_pre(self,xtrain,ytrain,xtest):
                # instantiated model
                pre_1 = SVR(C=10).fit(xtrain,ytrain).predict(xtest) # model_1
                pre_2 = SVR(C=50).fit(xtrain,ytrain).predict(xtest) # model_2
                pre_3 = SVR(C=80).fit(xtrain,ytrain).predict(xtest) # model_3
                model_1 , model_2 , model_3  can be changed to any ML models you desire
                # defined the attribute's outputs
                stacked_array = np.vstack((pre_1,pre_2,pre_3))
                means = np.mean(stacked_array, axis=0)
                std = np.sqrt(np.var(stacked_array), axis=0)
                return mean, std    

:param opt_num: the number of recommended candidates for next iteration, default 1. 

:param min_search: default True -> searching the global minimum ;
                           False -> searching the global maximum.

:param CV_test: 'LOOCV' or an int, default False (pass test) 
        if CV_test = 'LOOCV', LOOCV will be applied,
        elif CV_test = int, e.g., CV_test = 10, 10 folds cross validation will be applied.

:return: 1: array; potential of each candidate. 2: array/float; recommended candidate(s).
File:      ~/miniconda3/lib/python3.9/site-packages/Bgolearn/BGOsampling.py
Type:      method