566 lines
18 KiB
Python
566 lines
18 KiB
Python
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"""Base class for mixture models."""
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# Author: Wei Xue <xuewei4d@gmail.com>
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# Modified by Thierry Guillemot <thierry.guillemot.work@gmail.com>
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# License: BSD 3 clause
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import warnings
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from abc import ABCMeta, abstractmethod
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from numbers import Integral, Real
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from time import time
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import numpy as np
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from scipy.special import logsumexp
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from .. import cluster
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from ..base import BaseEstimator, DensityMixin, _fit_context
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from ..cluster import kmeans_plusplus
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from ..exceptions import ConvergenceWarning
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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.validation import check_is_fitted
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def _check_shape(param, param_shape, name):
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"""Validate the shape of the input parameter 'param'.
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Parameters
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----------
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param : array
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param_shape : tuple
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name : str
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"""
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param = np.array(param)
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if param.shape != param_shape:
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raise ValueError(
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"The parameter '%s' should have the shape of %s, but got %s"
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% (name, param_shape, param.shape)
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)
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class BaseMixture(DensityMixin, BaseEstimator, metaclass=ABCMeta):
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"""Base class for mixture models.
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This abstract class specifies an interface for all mixture classes and
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provides basic common methods for mixture models.
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"""
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_parameter_constraints: dict = {
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"n_components": [Interval(Integral, 1, None, closed="left")],
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"tol": [Interval(Real, 0.0, None, closed="left")],
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"reg_covar": [Interval(Real, 0.0, None, closed="left")],
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"max_iter": [Interval(Integral, 0, None, closed="left")],
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"n_init": [Interval(Integral, 1, None, closed="left")],
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"init_params": [
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StrOptions({"kmeans", "random", "random_from_data", "k-means++"})
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],
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"random_state": ["random_state"],
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"warm_start": ["boolean"],
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"verbose": ["verbose"],
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"verbose_interval": [Interval(Integral, 1, None, closed="left")],
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}
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def __init__(
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self,
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n_components,
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tol,
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reg_covar,
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max_iter,
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n_init,
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init_params,
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random_state,
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warm_start,
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verbose,
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verbose_interval,
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):
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self.n_components = n_components
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self.tol = tol
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self.reg_covar = reg_covar
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self.max_iter = max_iter
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self.n_init = n_init
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self.init_params = init_params
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self.random_state = random_state
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self.warm_start = warm_start
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self.verbose = verbose
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self.verbose_interval = verbose_interval
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@abstractmethod
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def _check_parameters(self, X):
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"""Check initial parameters of the derived class.
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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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"""
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pass
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def _initialize_parameters(self, X, random_state):
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"""Initialize the model parameters.
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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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random_state : RandomState
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A random number generator instance that controls the random seed
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used for the method chosen to initialize the parameters.
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"""
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n_samples, _ = X.shape
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if self.init_params == "kmeans":
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resp = np.zeros((n_samples, self.n_components))
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label = (
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cluster.KMeans(
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n_clusters=self.n_components, n_init=1, random_state=random_state
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)
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.fit(X)
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.labels_
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)
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resp[np.arange(n_samples), label] = 1
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elif self.init_params == "random":
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resp = random_state.uniform(size=(n_samples, self.n_components))
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resp /= resp.sum(axis=1)[:, np.newaxis]
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elif self.init_params == "random_from_data":
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resp = np.zeros((n_samples, self.n_components))
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indices = random_state.choice(
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n_samples, size=self.n_components, replace=False
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)
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resp[indices, np.arange(self.n_components)] = 1
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elif self.init_params == "k-means++":
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resp = np.zeros((n_samples, self.n_components))
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_, indices = kmeans_plusplus(
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X,
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self.n_components,
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random_state=random_state,
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)
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resp[indices, np.arange(self.n_components)] = 1
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self._initialize(X, resp)
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@abstractmethod
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def _initialize(self, X, resp):
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"""Initialize the model parameters of the derived class.
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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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resp : array-like of shape (n_samples, n_components)
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"""
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pass
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def fit(self, X, y=None):
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"""Estimate model parameters with the EM algorithm.
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The method fits the model ``n_init`` times and sets the parameters with
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which the model has the largest likelihood or lower bound. Within each
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trial, the method iterates between E-step and M-step for ``max_iter``
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times until the change of likelihood or lower bound is less than
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``tol``, otherwise, a ``ConvergenceWarning`` is raised.
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If ``warm_start`` is ``True``, then ``n_init`` is ignored and a single
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initialization is performed upon the first call. Upon consecutive
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calls, training starts where it left off.
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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 : Ignored
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Not used, present for API consistency by convention.
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Returns
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-------
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self : object
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The fitted mixture.
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"""
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# parameters are validated in fit_predict
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self.fit_predict(X, y)
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return self
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@_fit_context(prefer_skip_nested_validation=True)
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def fit_predict(self, X, y=None):
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"""Estimate model parameters using X and predict the labels for X.
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The method fits the model n_init times and sets the parameters with
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which the model has the largest likelihood or lower bound. Within each
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trial, the method iterates between E-step and M-step for `max_iter`
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times until the change of likelihood or lower bound is less than
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`tol`, otherwise, a :class:`~sklearn.exceptions.ConvergenceWarning` is
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raised. After fitting, it predicts the most probable label for the
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input data points.
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.. versionadded:: 0.20
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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 : Ignored
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Not used, present for API consistency by convention.
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Returns
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-------
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labels : array, shape (n_samples,)
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Component labels.
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"""
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X = self._validate_data(X, dtype=[np.float64, np.float32], ensure_min_samples=2)
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if X.shape[0] < self.n_components:
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raise ValueError(
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"Expected n_samples >= n_components "
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f"but got n_components = {self.n_components}, "
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f"n_samples = {X.shape[0]}"
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)
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self._check_parameters(X)
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# if we enable warm_start, we will have a unique initialisation
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do_init = not (self.warm_start and hasattr(self, "converged_"))
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n_init = self.n_init if do_init else 1
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max_lower_bound = -np.inf
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self.converged_ = False
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random_state = check_random_state(self.random_state)
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n_samples, _ = X.shape
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for init in range(n_init):
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self._print_verbose_msg_init_beg(init)
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if do_init:
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self._initialize_parameters(X, random_state)
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lower_bound = -np.inf if do_init else self.lower_bound_
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if self.max_iter == 0:
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best_params = self._get_parameters()
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best_n_iter = 0
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else:
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converged = False
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for n_iter in range(1, self.max_iter + 1):
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prev_lower_bound = lower_bound
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log_prob_norm, log_resp = self._e_step(X)
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self._m_step(X, log_resp)
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lower_bound = self._compute_lower_bound(log_resp, log_prob_norm)
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change = lower_bound - prev_lower_bound
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self._print_verbose_msg_iter_end(n_iter, change)
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if abs(change) < self.tol:
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converged = True
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break
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self._print_verbose_msg_init_end(lower_bound, converged)
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if lower_bound > max_lower_bound or max_lower_bound == -np.inf:
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max_lower_bound = lower_bound
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best_params = self._get_parameters()
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best_n_iter = n_iter
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self.converged_ = converged
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# Should only warn about convergence if max_iter > 0, otherwise
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# the user is assumed to have used 0-iters initialization
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# to get the initial means.
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if not self.converged_ and self.max_iter > 0:
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warnings.warn(
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(
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"Best performing initialization did not converge. "
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"Try different init parameters, or increase max_iter, "
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"tol, or check for degenerate data."
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),
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ConvergenceWarning,
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)
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self._set_parameters(best_params)
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self.n_iter_ = best_n_iter
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self.lower_bound_ = max_lower_bound
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# Always do a final e-step to guarantee that the labels returned by
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# fit_predict(X) are always consistent with fit(X).predict(X)
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# for any value of max_iter and tol (and any random_state).
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_, log_resp = self._e_step(X)
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return log_resp.argmax(axis=1)
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def _e_step(self, X):
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"""E step.
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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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Returns
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-------
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log_prob_norm : float
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Mean of the logarithms of the probabilities of each sample in X
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log_responsibility : array, shape (n_samples, n_components)
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Logarithm of the posterior probabilities (or responsibilities) of
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the point of each sample in X.
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"""
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log_prob_norm, log_resp = self._estimate_log_prob_resp(X)
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return np.mean(log_prob_norm), log_resp
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@abstractmethod
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def _m_step(self, X, log_resp):
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"""M step.
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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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log_resp : array-like of shape (n_samples, n_components)
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Logarithm of the posterior probabilities (or responsibilities) of
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the point of each sample in X.
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"""
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pass
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@abstractmethod
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def _get_parameters(self):
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pass
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@abstractmethod
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def _set_parameters(self, params):
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pass
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def score_samples(self, X):
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"""Compute the log-likelihood of each sample.
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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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Returns
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-------
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log_prob : array, shape (n_samples,)
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Log-likelihood of each sample in `X` under the current model.
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"""
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check_is_fitted(self)
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X = self._validate_data(X, reset=False)
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return logsumexp(self._estimate_weighted_log_prob(X), axis=1)
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def score(self, X, y=None):
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"""Compute the per-sample average log-likelihood of the given data X.
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Parameters
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----------
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X : array-like of shape (n_samples, n_dimensions)
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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 : Ignored
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Not used, present for API consistency by convention.
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Returns
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-------
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log_likelihood : float
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Log-likelihood of `X` under the Gaussian mixture model.
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"""
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return self.score_samples(X).mean()
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def predict(self, X):
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"""Predict the labels for the data samples in X using trained 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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Returns
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-------
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labels : array, shape (n_samples,)
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Component labels.
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"""
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check_is_fitted(self)
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X = self._validate_data(X, reset=False)
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return self._estimate_weighted_log_prob(X).argmax(axis=1)
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def predict_proba(self, X):
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"""Evaluate the components' density for each sample.
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Parameters
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|
----------
|
||
|
|
X : array-like of shape (n_samples, n_features)
|
||
|
|
List of n_features-dimensional data points. Each row
|
||
|
|
corresponds to a single data point.
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
resp : array, shape (n_samples, n_components)
|
||
|
|
Density of each Gaussian component for each sample in X.
|
||
|
|
"""
|
||
|
|
check_is_fitted(self)
|
||
|
|
X = self._validate_data(X, reset=False)
|
||
|
|
_, log_resp = self._estimate_log_prob_resp(X)
|
||
|
|
return np.exp(log_resp)
|
||
|
|
|
||
|
|
def sample(self, n_samples=1):
|
||
|
|
"""Generate random samples from the fitted Gaussian distribution.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
n_samples : int, default=1
|
||
|
|
Number of samples to generate.
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
X : array, shape (n_samples, n_features)
|
||
|
|
Randomly generated sample.
|
||
|
|
|
||
|
|
y : array, shape (nsamples,)
|
||
|
|
Component labels.
|
||
|
|
"""
|
||
|
|
check_is_fitted(self)
|
||
|
|
|
||
|
|
if n_samples < 1:
|
||
|
|
raise ValueError(
|
||
|
|
"Invalid value for 'n_samples': %d . The sampling requires at "
|
||
|
|
"least one sample." % (self.n_components)
|
||
|
|
)
|
||
|
|
|
||
|
|
_, n_features = self.means_.shape
|
||
|
|
rng = check_random_state(self.random_state)
|
||
|
|
n_samples_comp = rng.multinomial(n_samples, self.weights_)
|
||
|
|
|
||
|
|
if self.covariance_type == "full":
|
||
|
|
X = np.vstack(
|
||
|
|
[
|
||
|
|
rng.multivariate_normal(mean, covariance, int(sample))
|
||
|
|
for (mean, covariance, sample) in zip(
|
||
|
|
self.means_, self.covariances_, n_samples_comp
|
||
|
|
)
|
||
|
|
]
|
||
|
|
)
|
||
|
|
elif self.covariance_type == "tied":
|
||
|
|
X = np.vstack(
|
||
|
|
[
|
||
|
|
rng.multivariate_normal(mean, self.covariances_, int(sample))
|
||
|
|
for (mean, sample) in zip(self.means_, n_samples_comp)
|
||
|
|
]
|
||
|
|
)
|
||
|
|
else:
|
||
|
|
X = np.vstack(
|
||
|
|
[
|
||
|
|
mean
|
||
|
|
+ rng.standard_normal(size=(sample, n_features))
|
||
|
|
* np.sqrt(covariance)
|
||
|
|
for (mean, covariance, sample) in zip(
|
||
|
|
self.means_, self.covariances_, n_samples_comp
|
||
|
|
)
|
||
|
|
]
|
||
|
|
)
|
||
|
|
|
||
|
|
y = np.concatenate(
|
||
|
|
[np.full(sample, j, dtype=int) for j, sample in enumerate(n_samples_comp)]
|
||
|
|
)
|
||
|
|
|
||
|
|
return (X, y)
|
||
|
|
|
||
|
|
def _estimate_weighted_log_prob(self, X):
|
||
|
|
"""Estimate the weighted log-probabilities, log P(X | Z) + log weights.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
X : array-like of shape (n_samples, n_features)
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
weighted_log_prob : array, shape (n_samples, n_component)
|
||
|
|
"""
|
||
|
|
return self._estimate_log_prob(X) + self._estimate_log_weights()
|
||
|
|
|
||
|
|
@abstractmethod
|
||
|
|
def _estimate_log_weights(self):
|
||
|
|
"""Estimate log-weights in EM algorithm, E[ log pi ] in VB algorithm.
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
log_weight : array, shape (n_components, )
|
||
|
|
"""
|
||
|
|
pass
|
||
|
|
|
||
|
|
@abstractmethod
|
||
|
|
def _estimate_log_prob(self, X):
|
||
|
|
"""Estimate the log-probabilities log P(X | Z).
|
||
|
|
|
||
|
|
Compute the log-probabilities per each component for each sample.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
X : array-like of shape (n_samples, n_features)
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
log_prob : array, shape (n_samples, n_component)
|
||
|
|
"""
|
||
|
|
pass
|
||
|
|
|
||
|
|
def _estimate_log_prob_resp(self, X):
|
||
|
|
"""Estimate log probabilities and responsibilities for each sample.
|
||
|
|
|
||
|
|
Compute the log probabilities, weighted log probabilities per
|
||
|
|
component and responsibilities for each sample in X with respect to
|
||
|
|
the current state of the model.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
X : array-like of shape (n_samples, n_features)
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
log_prob_norm : array, shape (n_samples,)
|
||
|
|
log p(X)
|
||
|
|
|
||
|
|
log_responsibilities : array, shape (n_samples, n_components)
|
||
|
|
logarithm of the responsibilities
|
||
|
|
"""
|
||
|
|
weighted_log_prob = self._estimate_weighted_log_prob(X)
|
||
|
|
log_prob_norm = logsumexp(weighted_log_prob, axis=1)
|
||
|
|
with np.errstate(under="ignore"):
|
||
|
|
# ignore underflow
|
||
|
|
log_resp = weighted_log_prob - log_prob_norm[:, np.newaxis]
|
||
|
|
return log_prob_norm, log_resp
|
||
|
|
|
||
|
|
def _print_verbose_msg_init_beg(self, n_init):
|
||
|
|
"""Print verbose message on initialization."""
|
||
|
|
if self.verbose == 1:
|
||
|
|
print("Initialization %d" % n_init)
|
||
|
|
elif self.verbose >= 2:
|
||
|
|
print("Initialization %d" % n_init)
|
||
|
|
self._init_prev_time = time()
|
||
|
|
self._iter_prev_time = self._init_prev_time
|
||
|
|
|
||
|
|
def _print_verbose_msg_iter_end(self, n_iter, diff_ll):
|
||
|
|
"""Print verbose message on initialization."""
|
||
|
|
if n_iter % self.verbose_interval == 0:
|
||
|
|
if self.verbose == 1:
|
||
|
|
print(" Iteration %d" % n_iter)
|
||
|
|
elif self.verbose >= 2:
|
||
|
|
cur_time = time()
|
||
|
|
print(
|
||
|
|
" Iteration %d\t time lapse %.5fs\t ll change %.5f"
|
||
|
|
% (n_iter, cur_time - self._iter_prev_time, diff_ll)
|
||
|
|
)
|
||
|
|
self._iter_prev_time = cur_time
|
||
|
|
|
||
|
|
def _print_verbose_msg_init_end(self, lb, init_has_converged):
|
||
|
|
"""Print verbose message on the end of iteration."""
|
||
|
|
converged_msg = "converged" if init_has_converged else "did not converge"
|
||
|
|
if self.verbose == 1:
|
||
|
|
print(f"Initialization {converged_msg}.")
|
||
|
|
elif self.verbose >= 2:
|
||
|
|
t = time() - self._init_prev_time
|
||
|
|
print(
|
||
|
|
f"Initialization {converged_msg}. time lapse {t:.5f}s\t lower bound"
|
||
|
|
f" {lb:.5f}."
|
||
|
|
)
|