





from typing import Any






def    _A	(   lowerCamelCase				,			lowerCamelCase				,			lowerCamelCase				,			lowerCamelCase				,			lowerCamelCase				,			):
   _validation(
       lowerCamelCase				,			lowerCamelCase				,			lowerCamelCase				,			lowerCamelCase				,			lowerCamelCase				,			)
   # Creates data structures and fill initial step
   a__						:    dict   		=	{}
   a__						:    dict   		=	{}
   for state in states_space:
      a__						:    Any   		=	observations_space[0]
      a__						:    List[Any]   		=	(
          initial_probabilities[state] * emission_probabilities[state][observation]
      )
      a__						:    Any   		=	None

   # Fills the data structure with the probabilities of
   # different transitions and pointers to previous states
   for o in range(1				,			len(lowerCamelCase ) ):
      a__						:    Union[str, Any]   		=	observations_space[o]
      a__						:    Dict   		=	observations_space[o - 1]
      for state in states_space:
         # Calculates the argmax for probability function
         a__						:    Union[str, Any]   		=	""
         a__						:    Optional[int]   		=	-1
         for k_state in states_space:
            a__						:    Tuple   		=	(
                probabilities[(k_state, prior_observation)]
                * transition_probabilities[k_state][state]
                * emission_probabilities[state][observation]
            )
            if probability > max_probability:
               a__						:    Optional[int]   		=	probability
               a__						:    str   		=	k_state

            # Update probabilities and pointers dicts
         a__						:    Any   		=	(
             probabilities[(arg_max, prior_observation)]
             * transition_probabilities[arg_max][state]
             * emission_probabilities[state][observation]
         )

         a__						:    int   		=	arg_max

    # The final observation
   a__						:    Optional[Any]   		=	observations_space[len(lowerCamelCase ) - 1]

   # argmax for given final observation
   a__						:    Any   		=	""
   a__						:    Union[str, Any]   		=	-1
   for k_state in states_space:
      a__						:    Optional[Any]   		=	probabilities[(k_state, final_observation)]
      if probability > max_probability:
         a__						:    List[Any]   		=	probability
         a__						:    Any   		=	k_state
   a__						:    Union[str, Any]   		=	arg_max

   # Process pointers backwards
   a__						:    Union[str, Any]   		=	last_state
   a__						:    List[str]   		=	[]
   for o in range(len(lowerCamelCase ) - 1				,			-1				,			-1 ):
      result.append(lowerCamelCase )
      a__						:    Union[str, Any]   		=	pointers[previous, observations_space[o]]
   result.reverse()

   return result






def    _A	(   lowerCamelCase				,			lowerCamelCase				,			lowerCamelCase				,			lowerCamelCase				,			lowerCamelCase				,			):
   _validate_not_empty(
       lowerCamelCase				,			lowerCamelCase				,			lowerCamelCase				,			lowerCamelCase				,			lowerCamelCase				,			)
   _validate_lists(lowerCamelCase				,			lowerCamelCase )
   _validate_dicts(
       lowerCamelCase				,			lowerCamelCase				,			lowerCamelCase )






def    _A	(   lowerCamelCase				,			lowerCamelCase				,			lowerCamelCase				,			lowerCamelCase				,			lowerCamelCase				,			):
   if not all(
       [
           observations_space,
           states_space,
           initial_probabilities,
           transition_probabilities,
           emission_probabilities,
       ] ):
      raise ValueError("There's an empty parameter" )






def    _A	(   lowerCamelCase				,			lowerCamelCase ):
   _validate_list(lowerCamelCase				,			"observations_space" )
   _validate_list(lowerCamelCase				,			"states_space" )






def    _A	(   lowerCamelCase				,			lowerCamelCase ):
   if not isinstance(_object				,			lowerCamelCase ):
      a__						:    Union[str, Any]   		=	F"""{var_name} must be a list"""
      raise ValueError(lowerCamelCase )
   else:
      for x in _object:
         if not isinstance(lowerCamelCase				,			lowerCamelCase ):
            a__						:    int   		=	F"""{var_name} must be a list of strings"""
            raise ValueError(lowerCamelCase )






def    _A	(   lowerCamelCase				,			lowerCamelCase				,			lowerCamelCase				,			):
   _validate_dict(lowerCamelCase				,			"initial_probabilities"				,			lowerCamelCase )
   _validate_nested_dict(lowerCamelCase				,			"transition_probabilities" )
   _validate_nested_dict(lowerCamelCase				,			"emission_probabilities" )






def    _A	(   lowerCamelCase				,			lowerCamelCase ):
   _validate_dict(_object				,			lowerCamelCase				,			lowerCamelCase )
   for x in _object.values():
      _validate_dict(lowerCamelCase				,			lowerCamelCase				,			lowerCamelCase				,			lowerCamelCase )






def    _A	(   lowerCamelCase				,			lowerCamelCase				,			lowerCamelCase				,			lowerCamelCase = False ):
   if not isinstance(_object				,			lowerCamelCase ):
      a__						:    str   		=	F"""{var_name} must be a dict"""
      raise ValueError(lowerCamelCase )
   if not all(isinstance(lowerCamelCase				,			lowerCamelCase ) for x in _object ):
      a__						:    str   		=	F"""{var_name} all keys must be strings"""
      raise ValueError(lowerCamelCase )
   if not all(isinstance(lowerCamelCase				,			lowerCamelCase ) for x in _object.values() ):
      a__						:    List[str]   		=	"nested dictionary " if nested else ""
      a__						:    Union[str, Any]   		=	F"""{var_name} {nested_text}all values must be {value_type.__name__}"""
      raise ValueError(lowerCamelCase )


if __name__ == "__main__":
  from doctest import testmod

  testmod()








from sklearn.metrics import mean_squared_error

import datasets


SCREAMING_SNAKE_CASE__							:      List[str]         =    """\
@article{scikit-learn,
 title={Scikit-learn: Machine Learning in {P}ython},
 author={Pedregosa, F. and Varoquaux, G. and Gramfort, A. and Michel, V.
         and Thirion, B. and Grisel, O. and Blondel, M. and Prettenhofer, P.
         and Weiss, R. and Dubourg, V. and Vanderplas, J. and Passos, A. and
         Cournapeau, D. and Brucher, M. and Perrot, M. and Duchesnay, E.},
 journal={Journal of Machine Learning Research},
 volume={12},
 pages={2825--2830},
 year={2011}
}
"""

SCREAMING_SNAKE_CASE__							:      Tuple         =    """\
Mean Squared Error(MSE) is the average of the square of difference between the predicted
and actual values.
"""


SCREAMING_SNAKE_CASE__							:      Optional[Any]         =    """
Args:
    predictions: array-like of shape (n_samples,) or (n_samples, n_outputs)
        Estimated target values.
    references: array-like of shape (n_samples,) or (n_samples, n_outputs)
        Ground truth (correct) target values.
    sample_weight: array-like of shape (n_samples,), default=None
        Sample weights.
    multioutput: {\"raw_values\", \"uniform_average\"} or array-like of shape (n_outputs,), default=\"uniform_average\"
        Defines aggregating of multiple output values. Array-like value defines weights used to average errors.

        \"raw_values\" : Returns a full set of errors in case of multioutput input.

        \"uniform_average\" : Errors of all outputs are averaged with uniform weight.

    squared : bool, default=True
        If True returns MSE value, if False returns RMSE (Root Mean Squared Error) value.

Returns:
    mse : mean squared error.
Examples:

    >>> mse_metric = datasets.load_metric(\"mse\")
    >>> predictions = [2.5, 0.0, 2, 8]
    >>> references = [3, -0.5, 2, 7]
    >>> results = mse_metric.compute(predictions=predictions, references=references)
    >>> print(results)
    {'mse': 0.375}
    >>> rmse_result = mse_metric.compute(predictions=predictions, references=references, squared=False)
    >>> print(rmse_result)
    {'mse': 0.6123724356957945}

    If you're using multi-dimensional lists, then set the config as follows :

    >>> mse_metric = datasets.load_metric(\"mse\", \"multilist\")
    >>> predictions = [[0.5, 1], [-1, 1], [7, -6]]
    >>> references = [[0, 2], [-1, 2], [8, -5]]
    >>> results = mse_metric.compute(predictions=predictions, references=references)
    >>> print(results)
    {'mse': 0.7083333333333334}
    >>> results = mse_metric.compute(predictions=predictions, references=references, multioutput='raw_values')
    >>> print(results) # doctest: +NORMALIZE_WHITESPACE
    {'mse': array([0.41666667, 1. ])}
"""







@datasets.utils.file_utils.add_start_docstrings(_DESCRIPTION		,_KWARGS_DESCRIPTION	)
class 	__lowerCAmelCase      (       datasets.Metric	):





   def 						_snake_case			(			self   )					->	List[str]:
      """simple docstring"""





      return datasets.MetricInfo(
          description=_DESCRIPTION       ,      citation=_CITATION       ,      inputs_description=_KWARGS_DESCRIPTION       ,      features=datasets.Features(self._get_feature_types()   )       ,      reference_urls=[
              "https://scikit-learn.org/stable/modules/generated/sklearn.metrics.mean_squared_error.html"
          ]       ,      )





   def 						_snake_case			(			self   )					->	Optional[int]:
      """simple docstring"""





      if self.config_name == "multilist":
         return {
             "predictions": datasets.Sequence(datasets.Value("float"   )   ),
             "references": datasets.Sequence(datasets.Value("float"   )   ),
         }
      else:
         return {
             "predictions": datasets.Value("float"   ),
             "references": datasets.Value("float"   ),
         }





   def 						_snake_case			(			self       ,      snake_case       ,      snake_case       ,      snake_case=None       ,      snake_case="uniform_average"       ,      snake_case=True   )					->	Optional[Any]:
      """simple docstring"""





      a__						:    List[str]   		=	mean_squared_error(
          snake_case       ,      snake_case       ,      sample_weight=snake_case       ,      multioutput=snake_case       ,      squared=snake_case   )

      return {"mse": mse}

