_base.py

"""Base class for mixture models."""

# Author: Wei Xue <xuewei4d@gmail.com>
# Modified by Thierry Guillemot <thierry.guillemot.work@gmail.com>
# License: BSD 3 clause

import warnings
from abc import ABCMeta, abstractmethod
from time import time
from numbers import Integral, Real

import numpy as np
from scipy.special import logsumexp

from .. import cluster
from ..cluster import kmeans_plusplus
from ..base import BaseEstimator
from ..base import DensityMixin
from ..exceptions import ConvergenceWarning
from ..utils import check_random_state
from ..utils.validation import check_is_fitted
from ..utils._param_validation import Interval, StrOptions


def _check_shape(param, param_shape, name):
    """Validate the shape of the input parameter 'param'.

    Parameters
    ----------
    param : array

    param_shape : tuple

    name : str
    """
    param = np.array(param)
    if param.shape != param_shape:
        raise ValueError(
            "The parameter '%s' should have the shape of %s, but got %s"
            % (name, param_shape, param.shape)
        )


class BaseMixture(DensityMixin, BaseEstimator, metaclass=ABCMeta):
    """Base class for mixture models.

    This abstract class specifies an interface for all mixture classes and
    provides basic common methods for mixture models.
    """

    _parameter_constraints: dict = {
        "n_components": [Interval(Integral, 1, None, closed="left")],
        "tol": [Interval(Real, 0.0, None, closed="left")],
        "reg_covar": [Interval(Real, 0.0, None, closed="left")],
        "max_iter": [Interval(Integral, 0, None, closed="left")],
        "n_init": [Interval(Integral, 1, None, closed="left")],
        "init_params": [
            StrOptions({"kmeans", "random", "random_from_data", "k-means++"})
        ],
        "random_state": ["random_state"],
        "warm_start": ["boolean"],
        "verbose": ["verbose"],
        "verbose_interval": [Interval(Integral, 1, None, closed="left")],
    }

    def __init__(
        self,
        n_components,
        tol,
        reg_covar,
        max_iter,
        n_init,
        init_params,
        random_state,
        warm_start,
        verbose,
        verbose_interval,
    ):
        self.n_components = n_components
        self.tol = tol
        self.reg_covar = reg_covar
        self.max_iter = max_iter
        self.n_init = n_init
        self.init_params = init_params
        self.random_state = random_state
        self.warm_start = warm_start
        self.verbose = verbose
        self.verbose_interval = verbose_interval

    @abstractmethod
    def _check_parameters(self, X):
        """Check initial parameters of the derived class.

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

    def _initialize_parameters(self, X, random_state):
        """Initialize the model parameters.

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

        random_state : RandomState
            A random number generator instance that controls the random seed
            used for the method chosen to initialize the parameters.
        """
        n_samples, _ = X.shape

        if self.init_params == "kmeans":
            resp = np.zeros((n_samples, self.n_components))
            label = (
                cluster.KMeans(
                    n_clusters=self.n_components, n_init=1, random_state=random_state
                )
                .fit(X)
                .labels_
            )
            resp[np.arange(n_samples), label] = 1
        elif self.init_params == "random":
            resp = random_state.uniform(size=(n_samples, self.n_components))
            resp /= resp.sum(axis=1)[:, np.newaxis]
        elif self.init_params == "random_from_data":
            resp = np.zeros((n_samples, self.n_components))
            indices = random_state.choice(
                n_samples, size=self.n_components, replace=False
            )
            resp[indices, np.arange(self.n_components)] = 1
        elif self.init_params == "k-means++":
            resp = np.zeros((n_samples, self.n_components))
            _, indices = kmeans_plusplus(
                X,
                self.n_components,
                random_state=random_state,
            )
            resp[indices, np.arange(self.n_components)] = 1
        else:
            raise ValueError(
                "Unimplemented initialization method '%s'" % self.init_params
            )

        self._initialize(X, resp)

    @abstractmethod
    def _initialize(self, X, resp):
        """Initialize the model parameters of the derived class.

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

        resp : array-like of shape (n_samples, n_components)
        """
        pass

    def fit(self, X, y=None):
        """Estimate model parameters with the EM algorithm.

        The method fits the model ``n_init`` times and sets the parameters with
        which the model has the largest likelihood or lower bound. Within each
        trial, the method iterates between E-step and M-step for ``max_iter``
        times until the change of likelihood or lower bound is less than
        ``tol``, otherwise, a ``ConvergenceWarning`` is raised.
        If ``warm_start`` is ``True``, then ``n_init`` is ignored and a single
        initialization is performed upon the first call. Upon consecutive
        calls, training starts where it left off.

        Parameters
        ----------
        X : array-like of shape (n_samples, n_features)
            List of n_features-dimensional data points. Each row
            corresponds to a single data point.

        y : Ignored
            Not used, present for API consistency by convention.

        Returns
        -------
        self : object
            The fitted mixture.
        """
        # parameters are validated in fit_predict
        self.fit_predict(X, y)
        return self

    def fit_predict(self, X, y=None):
        """Estimate model parameters using X and predict the labels for X.

        The method fits the model n_init times and sets the parameters with
        which the model has the largest likelihood or lower bound. Within each
        trial, the method iterates between E-step and M-step for `max_iter`
        times until the change of likelihood or lower bound is less than
        `tol`, otherwise, a :class:`~sklearn.exceptions.ConvergenceWarning` is
        raised. After fitting, it predicts the most probable label for the
        input data points.

        .. versionadded:: 0.20

        Parameters
        ----------
        X : array-like of shape (n_samples, n_features)
            List of n_features-dimensional data points. Each row
            corresponds to a single data point.

        y : Ignored
            Not used, present for API consistency by convention.

        Returns
        -------
        labels : array, shape (n_samples,)
            Component labels.
        """
        self._validate_params()

        X = self._validate_data(X, dtype=[np.float64, np.float32], ensure_min_samples=2)
        if X.shape[0] < self.n_components:
            raise ValueError(
                "Expected n_samples >= n_components "
                f"but got n_components = {self.n_components}, "
                f"n_samples = {X.shape[0]}"
            )
        self._check_parameters(X)

        # if we enable warm_start, we will have a unique initialisation
        do_init = not (self.warm_start and hasattr(self, "converged_"))
        n_init = self.n_init if do_init else 1

        max_lower_bound = -np.inf
        self.converged_ = False

        random_state = check_random_state(self.random_state)

        n_samples, _ = X.shape
        for init in range(n_init):
            self._print_verbose_msg_init_beg(init)

            if do_init:
                self._initialize_parameters(X, random_state)

            lower_bound = -np.inf if do_init else self.lower_bound_

            if self.max_iter == 0:
                best_params = self._get_parameters()
                best_n_iter = 0
            else:
                for n_iter in range(1, self.max_iter + 1):
                    prev_lower_bound = lower_bound

                    log_prob_norm, log_resp = self._e_step(X)
                    self._m_step(X, log_resp)
                    lower_bound = self._compute_lower_bound(log_resp, log_prob_norm)

                    change = lower_bound - prev_lower_bound
                    self._print_verbose_msg_iter_end(n_iter, change)

                    if abs(change) < self.tol:
                        self.converged_ = True
                        break

                self._print_verbose_msg_init_end(lower_bound)

                if lower_bound > max_lower_bound or max_lower_bound == -np.inf:
                    max_lower_bound = lower_bound
                    best_params = self._get_parameters()
                    best_n_iter = n_iter

        # Should only warn about convergence if max_iter > 0, otherwise
        # the user is assumed to have used 0-iters initialization
        # to get the initial means.
        if not self.converged_ and self.max_iter > 0:
            warnings.warn(
                "Initialization %d did not converge. "
                "Try different init parameters, "
                "or increase max_iter, tol "
                "or check for degenerate data." % (init + 1),
                ConvergenceWarning,
            )

        self._set_parameters(best_params)
        self.n_iter_ = best_n_iter
        self.lower_bound_ = max_lower_bound

        # Always do a final e-step to guarantee that the labels returned by
        # fit_predict(X) are always consistent with fit(X).predict(X)
        # for any value of max_iter and tol (and any random_state).
        _, log_resp = self._e_step(X)

        return log_resp.argmax(axis=1)

    def _e_step(self, X):
        """E step.

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

        Returns
        -------
        log_prob_norm : float
            Mean of the logarithms of the probabilities of each sample in X

        log_responsibility : array, shape (n_samples, n_components)
            Logarithm of the posterior probabilities (or responsibilities) of
            the point of each sample in X.
        """
        log_prob_norm, log_resp = self._estimate_log_prob_resp(X)
        return np.mean(log_prob_norm), log_resp

    @abstractmethod
    def _m_step(self, X, log_resp):
        """M step.

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

        log_resp : array-like of shape (n_samples, n_components)
            Logarithm of the posterior probabilities (or responsibilities) of
            the point of each sample in X.
        """
        pass

    @abstractmethod
    def _get_parameters(self):
        pass

    @abstractmethod
    def _set_parameters(self, params):
        pass

    def score_samples(self, X):
        """Compute the log-likelihood of each sample.

        Parameters
        ----------
        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
        -------
        log_prob : array, shape (n_samples,)
            Log-likelihood of each sample in `X` under the current model.
        """
        check_is_fitted(self)
        X = self._validate_data(X, reset=False)

        return logsumexp(self._estimate_weighted_log_prob(X), axis=1)

    def score(self, X, y=None):
        """Compute the per-sample average log-likelihood of the given data X.

        Parameters
        ----------
        X : array-like of shape (n_samples, n_dimensions)
            List of n_features-dimensional data points. Each row
            corresponds to a single data point.

        y : Ignored
            Not used, present for API consistency by convention.

        Returns
        -------
        log_likelihood : float
            Log-likelihood of `X` under the Gaussian mixture model.
        """
        return self.score_samples(X).mean()

    def predict(self, X):
        """Predict the labels for the data samples in X using trained model.

        Parameters
        ----------
        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
        -------
        labels : array, shape (n_samples,)
            Component labels.
        """
        check_is_fitted(self)
        X = self._validate_data(X, reset=False)
        return self._estimate_weighted_log_prob(X).argmax(axis=1)

    def predict_proba(self, X):
        """Evaluate the components' density for each sample.

        Parameters
        ----------
        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, ll):
        """Print verbose message on the end of iteration."""
        if self.verbose == 1:
            print("Initialization converged: %s" % self.converged_)
        elif self.verbose >= 2:
            print(
                "Initialization converged: %s\t time lapse %.5fs\t ll %.5f"
                % (self.converged_, time() - self._init_prev_time, ll)
            )