class_docstr: A class containing functions supporting quantile, poisson and gaussian regression, to be used as a mixin for some
  `RegressionModel` subclasses.
class_docstr_tok: ["A","class","containing","functions","supporting","quantile",",","poisson","and","gaussian","regression",",","to","be","used","as","a","mixin","for","some","`","RegressionModel","`","subclasses","."]
docstr: X is of shape (n_series * n_samples, n_regression_features)
docstr_tok: ["X","is","of","shape","(","n_series","*","n_samples",",","n_regression_features",")"]
code: def _predict_quantile(
      self,
      x: np.ndarray,
      num_samples: int,
      predict_likelihood_parameters: bool,
      **kwargs,
  ) -> np.ndarray:
      """
      X is of shape (n_series * n_samples, n_regression_features)
      """
      k = x.shape[0]
  
      # if predict_likelihood_parameters is True, all the quantiles must be predicted
      if num_samples == 1 and not predict_likelihood_parameters:
          # return median
          fitted = self._model_container[0.5]
          return fitted.predict(x, **kwargs).reshape(
              k, self.pred_dim, -1
          )
  
      model_outputs = []
      for quantile, fitted in self._model_container.items():
          self.model = fitted
          # model output has shape (n_series * n_samples, output_chunk_length, n_components)
          model_output = fitted.predict(x, **kwargs).reshape(
              k, self.pred_dim, -1
          )
          model_outputs.append(model_output)
      model_outputs = np.stack(model_outputs, axis=-1)
      # shape (n_series * n_samples, output_chunk_length, n_components, n_quantiles)
      return model_outputs
  
imports: from collections import OrderedDict
  from typing import Any, Callable, Dict, List, Optional, Sequence, Tuple, Union
  import numpy
  import pandas
  from sklearn.linear_model import LinearRegression
  from darts.logging import get_logger, raise_if, raise_if_not, raise_log
  from darts.models.forecasting.forecasting_model import GlobalForecastingModel
  from darts.timeseries import TimeSeries
  from darts.utils.data.tabularization import add_static_covariates_to_lagged_data, create_lagged_component_names, create_lagged_training_data
  from darts.utils.historical_forecasts import _check_optimizable_historical_forecasts_global_models, _optimized_historical_forecasts_all_points, _optimized_historical_forecasts_last_points_only, _process_historical_forecast_input
  from darts.utils.multioutput import MultiOutputRegressor
  from darts.utils.utils import _check_quantiles, get_single_series, seq2series, series2seq
label_desc: Use image node_id 5 for calling the _LikelihoodMixin obj's underlying member method code with example usage: obj._predict_quantile(x, num_samples, predict_likelihood_parameters) and returns: model_outputs, fitted