Statistical Data Exploration LAB

Grid search: metoda najbliższych sąsiadów - jeden parametr

W naszych poprzednich zadaniach istotną kwestią okazywało się przeszukiwanie przestrzeni parametrów określających dany klasyfikator - np. w przypadku metody najbliższych sąsiadów jedyną zmienną, którą sterowaliśmy była liczba najbliższych sąsiadów. Tę analizę możną wykonywac “na piechotę”, ale często łatwiej jest się odwołać do funkcji GridSearchCV(). Jak sama nazwa wskazuje, jej celem jest wykonanie CV na pewnej sitace, czyli zestawie parametrów.

Zaczynamy od nieśmiertelnych danych (trochę zmienionych):

import numpy as np
import pandas as pd

def draw_data(n1, n2, m1, m2, S1, S2):

    data1 = np.random.multivariate_normal(m1, S1, n1)
    data2 = np.random.multivariate_normal(m2, S2, n2)

    data = np.concatenate((data1, data2), axis = 0)
    data = pd.DataFrame(data, columns=["x", "y"])

    data["klasa"] = np.repeat([0, 1], [n1, n2])
    
    return data

m1, m2 = [-1, -1], [1, 1]
S1 = [[4, 0], [0, 4]]
S2 = [[4, 0], [0, 4]]
n1, n2 = 60, 40

np.random.seed(129)
data = draw_data(n1, n2, m1, m2, S1, S2)

Następnie uruchamiamy pakiety oraz określamy siatkę parametrów - na początku bedzie to po prostu liczba najbliższych sąsiadów:

from sklearn.model_selection import GridSearchCV
from sklearn.neighbors import KNeighborsClassifier

param_grid = {'n_neighbors': range(2, 22)}

Kolejnym krokiem jest wskazanie klasyfikatora oraz uruchomienie docelowej funkcji

clf = KNeighborsClassifier()
clf_grid = GridSearchCV(clf, param_grid)
clf_grid.fit(data[["x", "y"]], data.klasa)

GridSearchCV(estimator=KNeighborsClassifier(),
             param_grid={'n_neighbors': range(2, 22)})

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Teraz przyjrzyjmy się wynikom, które kryja się pod clf.grid.cv_results_:

print(clf_grid.cv_results_)

## {'mean_fit_time': array([0.00103087, 0.00086465, 0.00088787, 0.00104766, 0.00090022,
##        0.00097637, 0.00086799, 0.00093455, 0.00082698, 0.00091963,
##        0.00082917, 0.00086117, 0.00082784, 0.00081258, 0.000811  ,
##        0.00125141, 0.00097685, 0.00085316, 0.00079618, 0.00088997]), 'std_fit_time': array([1.80731247e-04, 7.13216099e-05, 5.15489419e-05, 3.22793589e-04,
##        1.59487695e-04, 1.63889798e-04, 5.10796101e-05, 8.93312642e-05,
##        1.39922256e-05, 1.90570248e-04, 3.73005543e-05, 6.37436940e-05,
##        2.84801546e-05, 7.93099323e-06, 9.75432152e-06, 7.41339366e-04,
##        2.01895713e-04, 1.10031515e-04, 2.46206868e-06, 1.70189147e-04]), 'mean_score_time': array([0.00160389, 0.00129361, 0.0015862 , 0.00127063, 0.00130925,
##        0.00146461, 0.00137863, 0.00145402, 0.00131855, 0.00137696,
##        0.00128679, 0.0013298 , 0.00129609, 0.0012548 , 0.00124326,
##        0.00160637, 0.00145893, 0.0014195 , 0.00132179, 0.00135555]), 'std_score_time': array([2.70354197e-04, 1.01480694e-04, 3.94514357e-04, 6.81018956e-05,
##        4.90082366e-05, 1.06534535e-04, 1.54411667e-04, 2.62227863e-04,
##        1.55602245e-04, 1.55494440e-04, 9.28267850e-05, 1.09807802e-04,
##        3.72319143e-05, 3.14712524e-05, 3.88447014e-05, 5.05244300e-04,
##        2.25398327e-04, 3.63612374e-04, 1.73930234e-04, 1.15898957e-04]), 'param_n_neighbors': masked_array(data=[2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17,
##                    18, 19, 20, 21],
##              mask=[False, False, False, False, False, False, False, False,
##                    False, False, False, False, False, False, False, False,
##                    False, False, False, False],
##        fill_value=999999), 'params': [{'n_neighbors': 2}, {'n_neighbors': 3}, {'n_neighbors': 4}, {'n_neighbors': 5}, {'n_neighbors': 6}, {'n_neighbors': 7}, {'n_neighbors': 8}, {'n_neighbors': 9}, {'n_neighbors': 10}, {'n_neighbors': 11}, {'n_neighbors': 12}, {'n_neighbors': 13}, {'n_neighbors': 14}, {'n_neighbors': 15}, {'n_neighbors': 16}, {'n_neighbors': 17}, {'n_neighbors': 18}, {'n_neighbors': 19}, {'n_neighbors': 20}, {'n_neighbors': 21}], 'split0_test_score': array([0.8 , 0.8 , 0.75, 0.75, 0.85, 0.8 , 0.9 , 0.85, 0.85, 0.85, 0.9 ,
##        0.9 , 0.9 , 0.9 , 0.85, 0.85, 0.85, 0.85, 0.85, 0.85]), 'split1_test_score': array([0.9 , 0.8 , 0.9 , 0.9 , 0.9 , 0.9 , 0.9 , 0.95, 0.9 , 0.9 , 0.9 ,
##        0.95, 0.9 , 0.9 , 0.9 , 0.9 , 0.85, 0.9 , 0.9 , 0.9 ]), 'split2_test_score': array([0.7 , 0.65, 0.7 , 0.8 , 0.8 , 0.75, 0.8 , 0.8 , 0.8 , 0.8 , 0.8 ,
##        0.8 , 0.85, 0.85, 0.85, 0.85, 0.9 , 0.85, 0.85, 0.85]), 'split3_test_score': array([0.7 , 0.75, 0.75, 0.75, 0.75, 0.75, 0.8 , 0.8 , 0.75, 0.75, 0.75,
##        0.8 , 0.75, 0.85, 0.8 , 0.85, 0.85, 0.85, 0.85, 0.85]), 'split4_test_score': array([0.8 , 0.75, 0.8 , 0.8 , 0.8 , 0.85, 0.85, 0.85, 0.85, 0.9 , 0.85,
##        0.9 , 0.9 , 0.9 , 0.85, 0.85, 0.75, 0.8 , 0.7 , 0.75]), 'mean_test_score': array([0.78, 0.75, 0.78, 0.8 , 0.82, 0.81, 0.85, 0.85, 0.83, 0.84, 0.84,
##        0.87, 0.86, 0.88, 0.85, 0.86, 0.84, 0.85, 0.83, 0.84]), 'std_test_score': array([0.07483315, 0.05477226, 0.0678233 , 0.05477226, 0.0509902 ,
##        0.05830952, 0.04472136, 0.05477226, 0.0509902 , 0.05830952,
##        0.05830952, 0.06      , 0.05830952, 0.0244949 , 0.03162278,
##        0.02      , 0.04898979, 0.03162278, 0.0678233 , 0.04898979]), 'rank_test_score': array([18, 20, 19, 17, 15, 16,  5,  8, 14,  9,  9,  2,  3,  1,  5,  3,  9,
##         5, 13,  9], dtype=int32)}

Jest to dość sporo danych. Dla nas najważniejsza jest kwestia jakości (skuteczności) klasyfikatora mierzonego za pomocą wyniku kroswalidacji. Możemy to przedstawić za pomocą prostego wykresu:

import matplotlib.pyplot as plt

plt.errorbar(param_grid["n_neighbors"], clf_grid.cv_results_["mean_test_score"], clf_grid.cv_results_["std_test_score"], fmt="o", capsize=4)
plt.ylim(0.5, 1)

## (0.5, 1.0)

plt.xlabel("liczba najbliższych sąsiadów")
plt.ylabel("wynik CV")
plt.xticks(range(2, 22));

plt.show()

Aby uzyskać informację dla jakiego parametru przeszukiwanie dostrarczyło najlepszą wartość CV, odwołujemy się do:

print(clf_grid.best_params_, clf_grid.best_score_)

## {'n_neighbors': 15} 0.8800000000000001

Oczywiście jest to dość dyskusyjna sprawa, czy powinniśmy wybrać akurat taką wartość parametry, jeśli weźmiemy pod uwagę słupki niepewności.

	estimator estimator: estimator object This is assumed to implement the scikit-learn estimator interface. Either estimator needs to provide a ``score`` function, or ``scoring`` must be passed.	KNeighborsClassifier()
	param_grid param_grid: dict or list of dictionaries Dictionary with parameters names (`str`) as keys and lists of parameter settings to try as values, or a list of such dictionaries, in which case the grids spanned by each dictionary in the list are explored. This enables searching over any sequence of parameter settings.	{'n_neighbors': range(2, 22)}
	scoring scoring: str, callable, list, tuple or dict, default=None Strategy to evaluate the performance of the cross-validated model on the test set. If `scoring` represents a single score, one can use: - a single string (see :ref:`scoring_string_names`); - a callable (see :ref:`scoring_callable`) that returns a single value; - `None`, the `estimator`'s :ref:`default evaluation criterion ` is used. If `scoring` represents multiple scores, one can use: - a list or tuple of unique strings; - a callable returning a dictionary where the keys are the metric names and the values are the metric scores; - a dictionary with metric names as keys and callables as values. See :ref:`multimetric_grid_search` for an example.	None
	n_jobs n_jobs: int, default=None Number of jobs to run in parallel. ``None`` means 1 unless in a :obj:`joblib.parallel_backend` context. ``-1`` means using all processors. See :term:`Glossary ` for more details. .. versionchanged:: v0.20 `n_jobs` default changed from 1 to None	None
	refit refit: bool, str, or callable, default=True Refit an estimator using the best found parameters on the whole dataset. For multiple metric evaluation, this needs to be a `str` denoting the scorer that would be used to find the best parameters for refitting the estimator at the end. Where there are considerations other than maximum score in choosing a best estimator, ``refit`` can be set to a function which returns the selected ``best_index_`` given ``cv_results_``. In that case, the ``best_estimator_`` and ``best_params_`` will be set according to the returned ``best_index_`` while the ``best_score_`` attribute will not be available. The refitted estimator is made available at the ``best_estimator_`` attribute and permits using ``predict`` directly on this ``GridSearchCV`` instance. Also for multiple metric evaluation, the attributes ``best_index_``, ``best_score_`` and ``best_params_`` will only be available if ``refit`` is set and all of them will be determined w.r.t this specific scorer. See ``scoring`` parameter to know more about multiple metric evaluation. See :ref:`sphx_glr_auto_examples_model_selection_plot_grid_search_digits.py` to see how to design a custom selection strategy using a callable via `refit`. See :ref:`this example ` for an example of how to use ``refit=callable`` to balance model complexity and cross-validated score. .. versionchanged:: 0.20 Support for callable added.	True
	cv cv: int, cross-validation generator or an iterable, default=None Determines the cross-validation splitting strategy. Possible inputs for cv are: - None, to use the default 5-fold cross validation, - integer, to specify the number of folds in a `(Stratified)KFold`, - :term:`CV splitter`, - An iterable yielding (train, test) splits as arrays of indices. For integer/None inputs, if the estimator is a classifier and ``y`` is either binary or multiclass, :class:`StratifiedKFold` is used. In all other cases, :class:`KFold` is used. These splitters are instantiated with `shuffle=False` so the splits will be the same across calls. Refer :ref:`User Guide ` for the various cross-validation strategies that can be used here. .. versionchanged:: 0.22 ``cv`` default value if None changed from 3-fold to 5-fold.	None
	verbose verbose: int Controls the verbosity: the higher, the more messages. - >1 : the computation time for each fold and parameter candidate is displayed; - >2 : the score is also displayed; - >3 : the fold and candidate parameter indexes are also displayed together with the starting time of the computation.	0
	pre_dispatch pre_dispatch: int, or str, default='2n_jobs' Controls the number of jobs that get dispatched during parallel execution. Reducing this number can be useful to avoid an explosion of memory consumption when more jobs get dispatched than CPUs can process. This parameter can be: - None, in which case all the jobs are immediately created and spawned. Use this for lightweight and fast-running jobs, to avoid delays due to on-demand spawning of the jobs - An int, giving the exact number of total jobs that are spawned - A str, giving an expression as a function of n_jobs, as in '2n_jobs'	'2*n_jobs'
	error_score error_score: 'raise' or numeric, default=np.nan Value to assign to the score if an error occurs in estimator fitting. If set to 'raise', the error is raised. If a numeric value is given, FitFailedWarning is raised. This parameter does not affect the refit step, which will always raise the error.	nan
	return_train_score return_train_score: bool, default=False If ``False``, the ``cv_results_`` attribute will not include training scores. Computing training scores is used to get insights on how different parameter settings impact the overfitting/underfitting trade-off. However computing the scores on the training set can be computationally expensive and is not strictly required to select the parameters that yield the best generalization performance. .. versionadded:: 0.19 .. versionchanged:: 0.21 Default value was changed from ``True`` to ``False``	False

	n_neighbors n_neighbors: int, default=5 Number of neighbors to use by default for :meth:`kneighbors` queries.	15
	weights weights: {'uniform', 'distance'}, callable or None, default='uniform' Weight function used in prediction. Possible values: - 'uniform' : uniform weights. All points in each neighborhood are weighted equally. - 'distance' : weight points by the inverse of their distance. in this case, closer neighbors of a query point will have a greater influence than neighbors which are further away. - [callable] : a user-defined function which accepts an array of distances, and returns an array of the same shape containing the weights. Refer to the example entitled :ref:`sphx_glr_auto_examples_neighbors_plot_classification.py` showing the impact of the `weights` parameter on the decision boundary.	'uniform'
	algorithm algorithm: {'auto', 'ball_tree', 'kd_tree', 'brute'}, default='auto' Algorithm used to compute the nearest neighbors: - 'ball_tree' will use :class:`BallTree` - 'kd_tree' will use :class:`KDTree` - 'brute' will use a brute-force search. - 'auto' will attempt to decide the most appropriate algorithm based on the values passed to :meth:`fit` method. Note: fitting on sparse input will override the setting of this parameter, using brute force.	'auto'
	leaf_size leaf_size: int, default=30 Leaf size passed to BallTree or KDTree. This can affect the speed of the construction and query, as well as the memory required to store the tree. The optimal value depends on the nature of the problem.	30
	p p: float, default=2 Power parameter for the Minkowski metric. When p = 1, this is equivalent to using manhattan_distance (l1), and euclidean_distance (l2) for p = 2. For arbitrary p, minkowski_distance (l_p) is used. This parameter is expected to be positive.	2
	metric metric: str or callable, default='minkowski' Metric to use for distance computation. Default is "minkowski", which results in the standard Euclidean distance when p = 2. See the documentation of `scipy.spatial.distance `_ and the metrics listed in :class:`~sklearn.metrics.pairwise.distance_metrics` for valid metric values. If metric is "precomputed", X is assumed to be a distance matrix and must be square during fit. X may be a :term:`sparse graph`, in which case only "nonzero" elements may be considered neighbors. If metric is a callable function, it takes two arrays representing 1D vectors as inputs and must return one value indicating the distance between those vectors. This works for Scipy's metrics, but is less efficient than passing the metric name as a string.	'minkowski'
	metric_params metric_params: dict, default=None Additional keyword arguments for the metric function.	None
	n_jobs n_jobs: int, default=None The number of parallel jobs to run for neighbors search. ``None`` means 1 unless in a :obj:`joblib.parallel_backend` context. ``-1`` means using all processors. See :term:`Glossary ` for more details. Doesn't affect :meth:`fit` method.	None

	estimator estimator: estimator object This is assumed to implement the scikit-learn estimator interface. Either estimator needs to provide a ``score`` function, or ``scoring`` must be passed.	KNeighborsCla...'mahalanobis')
	param_grid param_grid: dict or list of dictionaries Dictionary with parameters names (`str`) as keys and lists of parameter settings to try as values, or a list of such dictionaries, in which case the grids spanned by each dictionary in the list are explored. This enables searching over any sequence of parameter settings.	{'metric_params': [{'V': [[2, 0], [0, 2]]}, {'V': [[2, 1], [1, 2]]}, ...], 'n_neighbors': range(2, 32)}
	scoring scoring: str, callable, list, tuple or dict, default=None Strategy to evaluate the performance of the cross-validated model on the test set. If `scoring` represents a single score, one can use: - a single string (see :ref:`scoring_string_names`); - a callable (see :ref:`scoring_callable`) that returns a single value; - `None`, the `estimator`'s :ref:`default evaluation criterion ` is used. If `scoring` represents multiple scores, one can use: - a list or tuple of unique strings; - a callable returning a dictionary where the keys are the metric names and the values are the metric scores; - a dictionary with metric names as keys and callables as values. See :ref:`multimetric_grid_search` for an example.	None
	n_jobs n_jobs: int, default=None Number of jobs to run in parallel. ``None`` means 1 unless in a :obj:`joblib.parallel_backend` context. ``-1`` means using all processors. See :term:`Glossary ` for more details. .. versionchanged:: v0.20 `n_jobs` default changed from 1 to None	None
	refit refit: bool, str, or callable, default=True Refit an estimator using the best found parameters on the whole dataset. For multiple metric evaluation, this needs to be a `str` denoting the scorer that would be used to find the best parameters for refitting the estimator at the end. Where there are considerations other than maximum score in choosing a best estimator, ``refit`` can be set to a function which returns the selected ``best_index_`` given ``cv_results_``. In that case, the ``best_estimator_`` and ``best_params_`` will be set according to the returned ``best_index_`` while the ``best_score_`` attribute will not be available. The refitted estimator is made available at the ``best_estimator_`` attribute and permits using ``predict`` directly on this ``GridSearchCV`` instance. Also for multiple metric evaluation, the attributes ``best_index_``, ``best_score_`` and ``best_params_`` will only be available if ``refit`` is set and all of them will be determined w.r.t this specific scorer. See ``scoring`` parameter to know more about multiple metric evaluation. See :ref:`sphx_glr_auto_examples_model_selection_plot_grid_search_digits.py` to see how to design a custom selection strategy using a callable via `refit`. See :ref:`this example ` for an example of how to use ``refit=callable`` to balance model complexity and cross-validated score. .. versionchanged:: 0.20 Support for callable added.	True
	cv cv: int, cross-validation generator or an iterable, default=None Determines the cross-validation splitting strategy. Possible inputs for cv are: - None, to use the default 5-fold cross validation, - integer, to specify the number of folds in a `(Stratified)KFold`, - :term:`CV splitter`, - An iterable yielding (train, test) splits as arrays of indices. For integer/None inputs, if the estimator is a classifier and ``y`` is either binary or multiclass, :class:`StratifiedKFold` is used. In all other cases, :class:`KFold` is used. These splitters are instantiated with `shuffle=False` so the splits will be the same across calls. Refer :ref:`User Guide ` for the various cross-validation strategies that can be used here. .. versionchanged:: 0.22 ``cv`` default value if None changed from 3-fold to 5-fold.	None
	verbose verbose: int Controls the verbosity: the higher, the more messages. - >1 : the computation time for each fold and parameter candidate is displayed; - >2 : the score is also displayed; - >3 : the fold and candidate parameter indexes are also displayed together with the starting time of the computation.	0
	pre_dispatch pre_dispatch: int, or str, default='2n_jobs' Controls the number of jobs that get dispatched during parallel execution. Reducing this number can be useful to avoid an explosion of memory consumption when more jobs get dispatched than CPUs can process. This parameter can be: - None, in which case all the jobs are immediately created and spawned. Use this for lightweight and fast-running jobs, to avoid delays due to on-demand spawning of the jobs - An int, giving the exact number of total jobs that are spawned - A str, giving an expression as a function of n_jobs, as in '2n_jobs'	'2*n_jobs'
	error_score error_score: 'raise' or numeric, default=np.nan Value to assign to the score if an error occurs in estimator fitting. If set to 'raise', the error is raised. If a numeric value is given, FitFailedWarning is raised. This parameter does not affect the refit step, which will always raise the error.	nan
	return_train_score return_train_score: bool, default=False If ``False``, the ``cv_results_`` attribute will not include training scores. Computing training scores is used to get insights on how different parameter settings impact the overfitting/underfitting trade-off. However computing the scores on the training set can be computationally expensive and is not strictly required to select the parameters that yield the best generalization performance. .. versionadded:: 0.19 .. versionchanged:: 0.21 Default value was changed from ``True`` to ``False``	False

	n_neighbors n_neighbors: int, default=5 Number of neighbors to use by default for :meth:`kneighbors` queries.	15
	weights weights: {'uniform', 'distance'}, callable or None, default='uniform' Weight function used in prediction. Possible values: - 'uniform' : uniform weights. All points in each neighborhood are weighted equally. - 'distance' : weight points by the inverse of their distance. in this case, closer neighbors of a query point will have a greater influence than neighbors which are further away. - [callable] : a user-defined function which accepts an array of distances, and returns an array of the same shape containing the weights. Refer to the example entitled :ref:`sphx_glr_auto_examples_neighbors_plot_classification.py` showing the impact of the `weights` parameter on the decision boundary.	'uniform'
	algorithm algorithm: {'auto', 'ball_tree', 'kd_tree', 'brute'}, default='auto' Algorithm used to compute the nearest neighbors: - 'ball_tree' will use :class:`BallTree` - 'kd_tree' will use :class:`KDTree` - 'brute' will use a brute-force search. - 'auto' will attempt to decide the most appropriate algorithm based on the values passed to :meth:`fit` method. Note: fitting on sparse input will override the setting of this parameter, using brute force.	'auto'
	leaf_size leaf_size: int, default=30 Leaf size passed to BallTree or KDTree. This can affect the speed of the construction and query, as well as the memory required to store the tree. The optimal value depends on the nature of the problem.	30
	p p: float, default=2 Power parameter for the Minkowski metric. When p = 1, this is equivalent to using manhattan_distance (l1), and euclidean_distance (l2) for p = 2. For arbitrary p, minkowski_distance (l_p) is used. This parameter is expected to be positive.	2
	metric metric: str or callable, default='minkowski' Metric to use for distance computation. Default is "minkowski", which results in the standard Euclidean distance when p = 2. See the documentation of `scipy.spatial.distance `_ and the metrics listed in :class:`~sklearn.metrics.pairwise.distance_metrics` for valid metric values. If metric is "precomputed", X is assumed to be a distance matrix and must be square during fit. X may be a :term:`sparse graph`, in which case only "nonzero" elements may be considered neighbors. If metric is a callable function, it takes two arrays representing 1D vectors as inputs and must return one value indicating the distance between those vectors. This works for Scipy's metrics, but is less efficient than passing the metric name as a string.	'mahalanobis'
	metric_params metric_params: dict, default=None Additional keyword arguments for the metric function.	{'V': [[2, 0], [0, 2]]}
	n_jobs n_jobs: int, default=None The number of parallel jobs to run for neighbors search. ``None`` means 1 unless in a :obj:`joblib.parallel_backend` context. ``-1`` means using all processors. See :term:`Glossary ` for more details. Doesn't affect :meth:`fit` method.	None

	criterion criterion: {"gini", "entropy", "log_loss"}, default="gini" The function to measure the quality of a split. Supported criteria are "gini" for the Gini impurity and "log_loss" and "entropy" both for the Shannon information gain, see :ref:`tree_mathematical_formulation`.	'gini'
	splitter splitter: {"best", "random"}, default="best" The strategy used to choose the split at each node. Supported strategies are "best" to choose the best split and "random" to choose the best random split.	'best'
	max_depth max_depth: int, default=None The maximum depth of the tree. If None, then nodes are expanded until all leaves are pure or until all leaves contain less than min_samples_split samples.	None
	min_samples_split min_samples_split: int or float, default=2 The minimum number of samples required to split an internal node: - If int, then consider `min_samples_split` as the minimum number. - If float, then `min_samples_split` is a fraction and `ceil(min_samples_split * n_samples)` are the minimum number of samples for each split. .. versionchanged:: 0.18 Added float values for fractions.	2
	min_samples_leaf min_samples_leaf: int or float, default=1 The minimum number of samples required to be at a leaf node. A split point at any depth will only be considered if it leaves at least ``min_samples_leaf`` training samples in each of the left and right branches. This may have the effect of smoothing the model, especially in regression. - If int, then consider `min_samples_leaf` as the minimum number. - If float, then `min_samples_leaf` is a fraction and `ceil(min_samples_leaf * n_samples)` are the minimum number of samples for each node. .. versionchanged:: 0.18 Added float values for fractions.	1
	min_weight_fraction_leaf min_weight_fraction_leaf: float, default=0.0 The minimum weighted fraction of the sum total of weights (of all the input samples) required to be at a leaf node. Samples have equal weight when sample_weight is not provided.	0.0
	max_features max_features: int, float or {"sqrt", "log2"}, default=None The number of features to consider when looking for the best split: - If int, then consider `max_features` features at each split. - If float, then `max_features` is a fraction and `max(1, int(max_features * n_features_in_))` features are considered at each split. - If "sqrt", then `max_features=sqrt(n_features)`. - If "log2", then `max_features=log2(n_features)`. - If None, then `max_features=n_features`. .. note:: The search for a split does not stop until at least one valid partition of the node samples is found, even if it requires to effectively inspect more than ``max_features`` features.	None
	random_state random_state: int, RandomState instance or None, default=None Controls the randomness of the estimator. The features are always randomly permuted at each split, even if ``splitter`` is set to ``"best"``. When ``max_features < n_features``, the algorithm will select ``max_features`` at random at each split before finding the best split among them. But the best found split may vary across different runs, even if ``max_features=n_features``. That is the case, if the improvement of the criterion is identical for several splits and one split has to be selected at random. To obtain a deterministic behaviour during fitting, ``random_state`` has to be fixed to an integer. See :term:`Glossary ` for details.	None
	max_leaf_nodes max_leaf_nodes: int, default=None Grow a tree with ``max_leaf_nodes`` in best-first fashion. Best nodes are defined as relative reduction in impurity. If None then unlimited number of leaf nodes.	None
	min_impurity_decrease min_impurity_decrease: float, default=0.0 A node will be split if this split induces a decrease of the impurity greater than or equal to this value. The weighted impurity decrease equation is the following:: N_t / N * (impurity - N_t_R / N_t * right_impurity - N_t_L / N_t * left_impurity) where ``N`` is the total number of samples, ``N_t`` is the number of samples at the current node, ``N_t_L`` is the number of samples in the left child, and ``N_t_R`` is the number of samples in the right child. ``N``, ``N_t``, ``N_t_R`` and ``N_t_L`` all refer to the weighted sum, if ``sample_weight`` is passed. .. versionadded:: 0.19	0.0
	class_weight class_weight: dict, list of dict or "balanced", default=None Weights associated with classes in the form ``{class_label: weight}``. If None, all classes are supposed to have weight one. For multi-output problems, a list of dicts can be provided in the same order as the columns of y. Note that for multioutput (including multilabel) weights should be defined for each class of every column in its own dict. For example, for four-class multilabel classification weights should be [{0: 1, 1: 1}, {0: 1, 1: 5}, {0: 1, 1: 1}, {0: 1, 1: 1}] instead of [{1:1}, {2:5}, {3:1}, {4:1}]. 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))`` For multi-output, the weights of each column of y will be multiplied. Note that these weights will be multiplied with sample_weight (passed through the fit method) if sample_weight is specified.	None
	ccp_alpha ccp_alpha: non-negative float, default=0.0 Complexity parameter used for Minimal Cost-Complexity Pruning. The subtree with the largest cost complexity that is smaller than ``ccp_alpha`` will be chosen. By default, no pruning is performed. See :ref:`minimal_cost_complexity_pruning` for details. See :ref:`sphx_glr_auto_examples_tree_plot_cost_complexity_pruning.py` for an example of such pruning. .. versionadded:: 0.22	0.0
	monotonic_cst monotonic_cst: array-like of int of shape (n_features), default=None Indicates the monotonicity constraint to enforce on each feature. - 1: monotonic increase - 0: no constraint - -1: monotonic decrease If monotonic_cst is None, no constraints are applied. Monotonicity constraints are not supported for: - multiclass classifications (i.e. when `n_classes > 2`), - multioutput classifications (i.e. when `n_outputs_ > 1`), - classifications trained on data with missing values. The constraints hold over the probability of the positive class. Read more in the :ref:`User Guide `. .. versionadded:: 1.4	None

Grid search: metoda najbliższych sąsiadów - jeden parametr

Grid search: metoda najbliższych sąsiadów - dwa parametry

Grid search: drzewa decyzyjne

Algorytm kosztu-złożoności

	estimator estimator: estimator object This is assumed to implement the scikit-learn estimator interface. Either estimator needs to provide a ``score`` function, or ``scoring`` must be passed.	DecisionTreeClassifier()
	param_grid param_grid: dict or list of dictionaries Dictionary with parameters names (`str`) as keys and lists of parameter settings to try as values, or a list of such dictionaries, in which case the grids spanned by each dictionary in the list are explored. This enables searching over any sequence of parameter settings.	{'max_leaf_nodes': range(2, 25)}
	scoring scoring: str, callable, list, tuple or dict, default=None Strategy to evaluate the performance of the cross-validated model on the test set. If `scoring` represents a single score, one can use: - a single string (see :ref:`scoring_string_names`); - a callable (see :ref:`scoring_callable`) that returns a single value; - `None`, the `estimator`'s :ref:`default evaluation criterion ` is used. If `scoring` represents multiple scores, one can use: - a list or tuple of unique strings; - a callable returning a dictionary where the keys are the metric names and the values are the metric scores; - a dictionary with metric names as keys and callables as values. See :ref:`multimetric_grid_search` for an example.	None
	n_jobs n_jobs: int, default=None Number of jobs to run in parallel. ``None`` means 1 unless in a :obj:`joblib.parallel_backend` context. ``-1`` means using all processors. See :term:`Glossary ` for more details. .. versionchanged:: v0.20 `n_jobs` default changed from 1 to None	None
	refit refit: bool, str, or callable, default=True Refit an estimator using the best found parameters on the whole dataset. For multiple metric evaluation, this needs to be a `str` denoting the scorer that would be used to find the best parameters for refitting the estimator at the end. Where there are considerations other than maximum score in choosing a best estimator, ``refit`` can be set to a function which returns the selected ``best_index_`` given ``cv_results_``. In that case, the ``best_estimator_`` and ``best_params_`` will be set according to the returned ``best_index_`` while the ``best_score_`` attribute will not be available. The refitted estimator is made available at the ``best_estimator_`` attribute and permits using ``predict`` directly on this ``GridSearchCV`` instance. Also for multiple metric evaluation, the attributes ``best_index_``, ``best_score_`` and ``best_params_`` will only be available if ``refit`` is set and all of them will be determined w.r.t this specific scorer. See ``scoring`` parameter to know more about multiple metric evaluation. See :ref:`sphx_glr_auto_examples_model_selection_plot_grid_search_digits.py` to see how to design a custom selection strategy using a callable via `refit`. See :ref:`this example ` for an example of how to use ``refit=callable`` to balance model complexity and cross-validated score. .. versionchanged:: 0.20 Support for callable added.	True
	cv cv: int, cross-validation generator or an iterable, default=None Determines the cross-validation splitting strategy. Possible inputs for cv are: - None, to use the default 5-fold cross validation, - integer, to specify the number of folds in a `(Stratified)KFold`, - :term:`CV splitter`, - An iterable yielding (train, test) splits as arrays of indices. For integer/None inputs, if the estimator is a classifier and ``y`` is either binary or multiclass, :class:`StratifiedKFold` is used. In all other cases, :class:`KFold` is used. These splitters are instantiated with `shuffle=False` so the splits will be the same across calls. Refer :ref:`User Guide ` for the various cross-validation strategies that can be used here. .. versionchanged:: 0.22 ``cv`` default value if None changed from 3-fold to 5-fold.	None
	verbose verbose: int Controls the verbosity: the higher, the more messages. - >1 : the computation time for each fold and parameter candidate is displayed; - >2 : the score is also displayed; - >3 : the fold and candidate parameter indexes are also displayed together with the starting time of the computation.	0
	pre_dispatch pre_dispatch: int, or str, default='2n_jobs' Controls the number of jobs that get dispatched during parallel execution. Reducing this number can be useful to avoid an explosion of memory consumption when more jobs get dispatched than CPUs can process. This parameter can be: - None, in which case all the jobs are immediately created and spawned. Use this for lightweight and fast-running jobs, to avoid delays due to on-demand spawning of the jobs - An int, giving the exact number of total jobs that are spawned - A str, giving an expression as a function of n_jobs, as in '2n_jobs'	'2*n_jobs'
	error_score error_score: 'raise' or numeric, default=np.nan Value to assign to the score if an error occurs in estimator fitting. If set to 'raise', the error is raised. If a numeric value is given, FitFailedWarning is raised. This parameter does not affect the refit step, which will always raise the error.	nan
	return_train_score return_train_score: bool, default=False If ``False``, the ``cv_results_`` attribute will not include training scores. Computing training scores is used to get insights on how different parameter settings impact the overfitting/underfitting trade-off. However computing the scores on the training set can be computationally expensive and is not strictly required to select the parameters that yield the best generalization performance. .. versionadded:: 0.19 .. versionchanged:: 0.21 Default value was changed from ``True`` to ``False``	False