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

from __future__ import print_function

import warnings
from abc import ABCMeta, abstractmethod
from time import time

import numpy as np

from .. import cluster
from ..base import BaseEstimator
from ..base import DensityMixin
from ..externals import six
from ..exceptions import ConvergenceWarning
from ..utils import check_array, check_random_state
from ..utils.fixes import logsumexp


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

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

    param_shape : tuple

    name : string
    """
    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))


def _check_X(X, n_components=None, n_features=None, ensure_min_samples=1):
    """Check the input data X.

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

    n_components : int

    Returns
    -------
    X : array, shape (n_samples, n_features)
    """
    X = check_array(X, dtype=[np.float64, np.float32],
                    ensure_min_samples=ensure_min_samples)
    if n_components is not None and X.shape[0] < n_components:
        raise ValueError('Expected n_samples >= n_components '
                         'but got n_components = %d, n_samples = %d'
                         % (n_components, X.shape[0]))
    if n_features is not None and X.shape[1] != n_features:
        raise ValueError("Expected the input data X have %d features, "
                         "but got %d features"
                         % (n_features, X.shape[1]))
    return X


class BaseMixture(six.with_metaclass(ABCMeta, DensityMixin, BaseEstimator)):
    """Base class for mixture models.

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

    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

    def _check_initial_parameters(self, X):
        """Check values of the basic parameters.

        Parameters
        ----------
        X : array-like, shape (n_samples, n_features)
        """
        if self.n_components < 1:
            raise ValueError("Invalid value for 'n_components': %d "
                             "Estimation requires at least one component"
                             % self.n_components)

        if self.tol < 0.:
            raise ValueError("Invalid value for 'tol': %.5f "
                             "Tolerance used by the EM must be non-negative"
                             % self.tol)

        if self.n_init < 1:
            raise ValueError("Invalid value for 'n_init': %d "
                             "Estimation requires at least one run"
                             % self.n_init)

        if self.max_iter < 1:
            raise ValueError("Invalid value for 'max_iter': %d "
                             "Estimation requires at least one iteration"
                             % self.max_iter)

        if self.reg_covar < 0.:
            raise ValueError("Invalid value for 'reg_covar': %.5f "
                             "regularization on covariance must be "
                             "non-negative"
                             % self.reg_covar)

        # Check all the parameters values of the derived class
        self._check_parameters(X)

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

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

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

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

        random_state : RandomState
            A random number generator instance.
        """
        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.rand(n_samples, self.n_components)
            resp /= resp.sum(axis=1)[:, np.newaxis]
        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, shape  (n_samples, n_features)

        resp : array-like, 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 set 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.

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

        Returns
        -------
        self
        """
        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 `ConvergenceWarning` is raised. After fitting, it
        predicts the most probable label for the input data points.

        .. versionadded:: 0.20

        Parameters
        ----------
        X : array-like, 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.
        """
        X = _check_X(X, self.n_components, ensure_min_samples=2)
        self._check_initial_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.infty
        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)
                self.lower_bound_ = -np.infty

            for n_iter in range(1, self.max_iter + 1):
                prev_lower_bound = self.lower_bound_

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

                change = self.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(self.lower_bound_)

            if self.lower_bound_ > max_lower_bound:
                max_lower_bound = self.lower_bound_
                best_params = self._get_parameters()
                best_n_iter = n_iter

        if not self.converged_:
            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

        return log_resp.argmax(axis=1)

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

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

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

    @abstractmethod
    def _check_is_fitted(self):
        pass

    @abstractmethod
    def _get_parameters(self):
        pass

    @abstractmethod
    def _set_parameters(self, params):
        pass

    def score_samples(self, X):
        """Compute the weighted log probabilities for each sample.

        Parameters
        ----------
        X : array-like, 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 probabilities of each data point in X.
        """
        self._check_is_fitted()
        X = _check_X(X, None, self.means_.shape[1])

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

        Returns
        -------
        log_likelihood : float
            Log likelihood of the Gaussian mixture given X.
        """
        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, 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.
        """
        self._check_is_fitted()
        X = _check_X(X, None, self.means_.shape[1])
        return self._estimate_weighted_log_prob(X).argmax(axis=1)

    def predict_proba(self, X):
        """Predict posterior probability of each component given the data.

        Parameters
        ----------
        X : array-like, 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)
            Returns the probability each Gaussian (state) in
            the model given each sample.
        """
        self._check_is_fitted()
        X = _check_X(X, None, self.means_.shape[1])
        _, 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, optional
            Number of samples to generate. Defaults to 1.

        Returns
        -------
        X : array, shape (n_samples, n_features)
            Randomly generated sample

        y : array, shape (nsamples,)
            Component labels

        """
        self._check_is_fitted()

        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.randn(sample, n_features) * np.sqrt(covariance)
                for (mean, covariance, sample) in zip(
                    self.means_, self.covariances_, n_samples_comp)])

        y = np.concatenate([j * np.ones(sample, 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, 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, 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, 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))