367 lines
12 KiB
Python
367 lines
12 KiB
Python
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"""
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Kernel Density Estimation
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-------------------------
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"""
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# Author: Jake Vanderplas <jakevdp@cs.washington.edu>
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import itertools
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from numbers import Integral, Real
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import numpy as np
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from scipy.special import gammainc
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from ..base import BaseEstimator, _fit_context
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from ..neighbors._base import VALID_METRICS
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from ..utils import check_random_state
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from ..utils._param_validation import Interval, StrOptions
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from ..utils.extmath import row_norms
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from ..utils.validation import _check_sample_weight, check_is_fitted
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from ._ball_tree import BallTree
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from ._kd_tree import KDTree
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VALID_KERNELS = [
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"gaussian",
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"tophat",
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"epanechnikov",
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"exponential",
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"linear",
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"cosine",
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]
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TREE_DICT = {"ball_tree": BallTree, "kd_tree": KDTree}
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# TODO: implement a brute force version for testing purposes
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# TODO: create a density estimation base class?
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class KernelDensity(BaseEstimator):
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"""Kernel Density Estimation.
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Read more in the :ref:`User Guide <kernel_density>`.
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Parameters
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----------
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bandwidth : float or {"scott", "silverman"}, default=1.0
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The bandwidth of the kernel. If bandwidth is a float, it defines the
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bandwidth of the kernel. If bandwidth is a string, one of the estimation
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methods is implemented.
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algorithm : {'kd_tree', 'ball_tree', 'auto'}, default='auto'
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The tree algorithm to use.
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kernel : {'gaussian', 'tophat', 'epanechnikov', 'exponential', 'linear', \
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'cosine'}, default='gaussian'
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The kernel to use.
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metric : str, default='euclidean'
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Metric to use for distance computation. See the
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documentation of `scipy.spatial.distance
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<https://docs.scipy.org/doc/scipy/reference/spatial.distance.html>`_ and
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the metrics listed in
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:class:`~sklearn.metrics.pairwise.distance_metrics` for valid metric
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values.
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Not all metrics are valid with all algorithms: refer to the
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documentation of :class:`BallTree` and :class:`KDTree`. Note that the
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normalization of the density output is correct only for the Euclidean
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distance metric.
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atol : float, default=0
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The desired absolute tolerance of the result. A larger tolerance will
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generally lead to faster execution.
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rtol : float, default=0
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The desired relative tolerance of the result. A larger tolerance will
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generally lead to faster execution.
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breadth_first : bool, default=True
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If true (default), use a breadth-first approach to the problem.
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Otherwise use a depth-first approach.
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leaf_size : int, default=40
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Specify the leaf size of the underlying tree. See :class:`BallTree`
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or :class:`KDTree` for details.
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metric_params : dict, default=None
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Additional parameters to be passed to the tree for use with the
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metric. For more information, see the documentation of
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:class:`BallTree` or :class:`KDTree`.
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Attributes
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----------
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n_features_in_ : int
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Number of features seen during :term:`fit`.
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.. versionadded:: 0.24
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tree_ : ``BinaryTree`` instance
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The tree algorithm for fast generalized N-point problems.
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feature_names_in_ : ndarray of shape (`n_features_in_`,)
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Names of features seen during :term:`fit`. Defined only when `X`
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has feature names that are all strings.
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bandwidth_ : float
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Value of the bandwidth, given directly by the bandwidth parameter or
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estimated using the 'scott' or 'silverman' method.
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.. versionadded:: 1.0
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See Also
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--------
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sklearn.neighbors.KDTree : K-dimensional tree for fast generalized N-point
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problems.
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sklearn.neighbors.BallTree : Ball tree for fast generalized N-point
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problems.
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Examples
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--------
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Compute a gaussian kernel density estimate with a fixed bandwidth.
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>>> from sklearn.neighbors import KernelDensity
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>>> import numpy as np
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>>> rng = np.random.RandomState(42)
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>>> X = rng.random_sample((100, 3))
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>>> kde = KernelDensity(kernel='gaussian', bandwidth=0.5).fit(X)
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>>> log_density = kde.score_samples(X[:3])
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>>> log_density
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array([-1.52955942, -1.51462041, -1.60244657])
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"""
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_parameter_constraints: dict = {
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"bandwidth": [
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Interval(Real, 0, None, closed="neither"),
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StrOptions({"scott", "silverman"}),
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],
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"algorithm": [StrOptions(set(TREE_DICT.keys()) | {"auto"})],
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"kernel": [StrOptions(set(VALID_KERNELS))],
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"metric": [
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StrOptions(
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set(itertools.chain(*[VALID_METRICS[alg] for alg in TREE_DICT.keys()]))
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)
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],
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"atol": [Interval(Real, 0, None, closed="left")],
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"rtol": [Interval(Real, 0, None, closed="left")],
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"breadth_first": ["boolean"],
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"leaf_size": [Interval(Integral, 1, None, closed="left")],
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"metric_params": [None, dict],
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}
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def __init__(
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self,
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*,
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bandwidth=1.0,
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algorithm="auto",
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kernel="gaussian",
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metric="euclidean",
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atol=0,
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rtol=0,
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breadth_first=True,
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leaf_size=40,
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metric_params=None,
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):
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self.algorithm = algorithm
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self.bandwidth = bandwidth
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self.kernel = kernel
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self.metric = metric
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self.atol = atol
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self.rtol = rtol
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self.breadth_first = breadth_first
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self.leaf_size = leaf_size
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self.metric_params = metric_params
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def _choose_algorithm(self, algorithm, metric):
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# given the algorithm string + metric string, choose the optimal
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# algorithm to compute the result.
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if algorithm == "auto":
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# use KD Tree if possible
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if metric in KDTree.valid_metrics:
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return "kd_tree"
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elif metric in BallTree.valid_metrics:
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return "ball_tree"
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else: # kd_tree or ball_tree
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if metric not in TREE_DICT[algorithm].valid_metrics:
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raise ValueError(
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"invalid metric for {0}: '{1}'".format(TREE_DICT[algorithm], metric)
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)
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return algorithm
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@_fit_context(
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# KernelDensity.metric is not validated yet
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prefer_skip_nested_validation=False
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)
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def fit(self, X, y=None, sample_weight=None):
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"""Fit the Kernel Density model on the data.
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Parameters
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----------
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X : array-like of shape (n_samples, n_features)
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List of n_features-dimensional data points. Each row
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corresponds to a single data point.
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y : None
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Ignored. This parameter exists only for compatibility with
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:class:`~sklearn.pipeline.Pipeline`.
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sample_weight : array-like of shape (n_samples,), default=None
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List of sample weights attached to the data X.
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.. versionadded:: 0.20
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Returns
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-------
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self : object
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Returns the instance itself.
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"""
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algorithm = self._choose_algorithm(self.algorithm, self.metric)
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if isinstance(self.bandwidth, str):
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if self.bandwidth == "scott":
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self.bandwidth_ = X.shape[0] ** (-1 / (X.shape[1] + 4))
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elif self.bandwidth == "silverman":
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self.bandwidth_ = (X.shape[0] * (X.shape[1] + 2) / 4) ** (
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-1 / (X.shape[1] + 4)
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)
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else:
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self.bandwidth_ = self.bandwidth
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X = self._validate_data(X, order="C", dtype=np.float64)
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if sample_weight is not None:
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sample_weight = _check_sample_weight(
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sample_weight, X, dtype=np.float64, only_non_negative=True
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)
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kwargs = self.metric_params
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if kwargs is None:
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kwargs = {}
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self.tree_ = TREE_DICT[algorithm](
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X,
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metric=self.metric,
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leaf_size=self.leaf_size,
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sample_weight=sample_weight,
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**kwargs,
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)
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return self
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def score_samples(self, X):
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"""Compute the log-likelihood of each sample under the model.
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Parameters
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----------
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X : array-like of shape (n_samples, n_features)
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An array of points to query. Last dimension should match dimension
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of training data (n_features).
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Returns
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-------
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density : ndarray of shape (n_samples,)
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Log-likelihood of each sample in `X`. These are normalized to be
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probability densities, so values will be low for high-dimensional
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data.
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"""
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check_is_fitted(self)
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# The returned density is normalized to the number of points.
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# For it to be a probability, we must scale it. For this reason
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# we'll also scale atol.
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X = self._validate_data(X, order="C", dtype=np.float64, reset=False)
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if self.tree_.sample_weight is None:
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N = self.tree_.data.shape[0]
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else:
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N = self.tree_.sum_weight
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atol_N = self.atol * N
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log_density = self.tree_.kernel_density(
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X,
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h=self.bandwidth_,
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kernel=self.kernel,
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atol=atol_N,
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rtol=self.rtol,
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breadth_first=self.breadth_first,
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return_log=True,
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)
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log_density -= np.log(N)
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return log_density
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def score(self, X, y=None):
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"""Compute the total log-likelihood under the model.
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Parameters
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----------
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X : array-like of shape (n_samples, n_features)
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List of n_features-dimensional data points. Each row
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corresponds to a single data point.
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y : None
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Ignored. This parameter exists only for compatibility with
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:class:`~sklearn.pipeline.Pipeline`.
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Returns
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-------
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logprob : float
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Total log-likelihood of the data in X. This is normalized to be a
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probability density, so the value will be low for high-dimensional
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data.
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"""
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return np.sum(self.score_samples(X))
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def sample(self, n_samples=1, random_state=None):
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"""Generate random samples from the model.
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Currently, this is implemented only for gaussian and tophat kernels.
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Parameters
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----------
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n_samples : int, default=1
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Number of samples to generate.
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random_state : int, RandomState instance or None, default=None
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Determines random number generation used to generate
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random samples. Pass an int for reproducible results
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across multiple function calls.
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See :term:`Glossary <random_state>`.
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Returns
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-------
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X : array-like of shape (n_samples, n_features)
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List of samples.
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"""
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check_is_fitted(self)
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# TODO: implement sampling for other valid kernel shapes
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if self.kernel not in ["gaussian", "tophat"]:
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raise NotImplementedError()
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data = np.asarray(self.tree_.data)
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rng = check_random_state(random_state)
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u = rng.uniform(0, 1, size=n_samples)
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if self.tree_.sample_weight is None:
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i = (u * data.shape[0]).astype(np.int64)
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else:
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cumsum_weight = np.cumsum(np.asarray(self.tree_.sample_weight))
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sum_weight = cumsum_weight[-1]
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i = np.searchsorted(cumsum_weight, u * sum_weight)
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if self.kernel == "gaussian":
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return np.atleast_2d(rng.normal(data[i], self.bandwidth_))
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elif self.kernel == "tophat":
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# we first draw points from a d-dimensional normal distribution,
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# then use an incomplete gamma function to map them to a uniform
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# d-dimensional tophat distribution.
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dim = data.shape[1]
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X = rng.normal(size=(n_samples, dim))
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s_sq = row_norms(X, squared=True)
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correction = (
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gammainc(0.5 * dim, 0.5 * s_sq) ** (1.0 / dim)
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* self.bandwidth_
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/ np.sqrt(s_sq)
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)
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return data[i] + X * correction[:, np.newaxis]
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def _more_tags(self):
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return {
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"_xfail_checks": {
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"check_sample_weights_invariance": (
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"sample_weight must have positive values"
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),
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}
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}
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