Return log-probability estimates for the test vector X.
        Parameters
        ----------
        X : array-like, shape = [n_samples, n_features]
        Returns
        -------
        C : array-like, shape = [n_samples, n_classes]
            Returns the log-probability of the samples for each class in
            the model. The columns correspond to the classes in sorted
            order, as they appear in the attribute `classes_`.

def predict_log_proba(self, X):
        """
        Return log-probability estimates for the test vector X.
        Parameters
        ----------
        X : array-like, shape = [n_samples, n_features]
        Returns
        -------
        C : array-like, shape = [n_samples, n_classes]
            Returns the log-probability of the samples for each class in
            the model. The columns correspond to the classes in sorted
            order, as they appear in the attribute `classes_`.
        """
        jll = self._joint_log_likelihood(X)
        # normalize by P(x) = P(f_1, ..., f_n)
        log_prob_x = logsumexp(jll, axis=1)
        return jll - log_prob_x.reshape(-1, 1)