Instance Methods

class pydtmc.HiddenMarkovModel[source]
decode(symbols, initial_status=None, use_scaling=True)[source]

The method calculates the log probability, the posterior probabilities, the backward probabilities and the forward probabilities of an observed sequence of symbols.

Notes:

  • If the observed sequence of symbols cannot be decoded, then None is returned.

Parameters:

  • symbols (Union[List[int], List[str]]) – the observed sequence of symbols.

  • initial_status (Optional[Union [int, str, ndarray, spmatrix]]) – the initial state or the initial distribution of the states (if omitted, the states are assumed to be uniformly distributed).

  • use_scaling (bool) – a boolean indicating whether to return scaled backward and forward probabilities together with their scaling factors.

Raises:

ValidationError – if any input argument is not compliant.

Return Type:

Optional[Tuple[float, ndarray, ndarray, ndarray, Optional[ndarray]]]

emission_probability(symbol, state)[source]

The method computes the probability of a given symbol, conditioned on the process being at a given state.

Parameters:
Raises:

ValidationError – if any input argument is not compliant.

Return Type:

float

next(initial_state, target='both', output_index=False, seed=None)[source]

The method simulates a single step in a random walk.

Parameters:

  • initial_state (Union[int, str]) – the initial state.

  • target (str)

    • state for a random state;

    • symbol for a random symbol;

    • both for a random state and a random symbol.

  • output_index (bool) – a boolean indicating whether to output the state index.

  • seed (Optional[int]) – a seed to be used as RNG initializer for reproducibility purposes.

Raises:

ValidationError – if any input argument is not compliant.

Return Type:

Union[int, str, Tuple[int, int], Tuple[str, str]]

predict(prediction_type, symbols, initial_status=None, output_indices=False)[source]

The method calculates the log probability and the most probable states path of an observed sequence of symbols.

Notes:

  • If the maximum a posteriori prediction is used and the observed sequence of symbols cannot be decoded, then None is returned.

  • If the maximum likelihood prediction is used and the observed sequence of symbols produces null transition probabilities, then None is returned.

Parameters:

  • prediction_type (str)

    • map for the maximum a posteriori prediction;

    • mle or viterbi for the maximum likelihood prediction.

  • symbols (Union[List[int], List[str]]) – the observed sequence of symbols.

  • initial_status (Optional[Union [int, str, ndarray, spmatrix]]) – the initial state or the initial distribution of the states (if omitted, the states are assumed to be uniformly distributed).

  • output_indices (bool) – a boolean indicating whether to output the state indices.

Raises:

ValidationError – if any input argument is not compliant.

Return Type:

Tuple[float, Union[List[int], List[str]]]

restrict(states=None, symbols=None)[source]

The method returns a submodel restricted to the given states and symbols.

Notes:

  • Submodel transition and emission matrices are normalized so that their rows sum to 1.0.

  • Submodel transition and emission matrices whose rows sum to 0.0 are replaced by uniformly distributed probabilities.

Parameters:
Raises:

ValidationError – if any input argument is not compliant.

Return Type:

HiddenMarkovModel

simulate(steps, initial_state=None, final_state=None, final_symbol=None, output_indices=False, seed=None)[source]

The method simulates a random sequence of states and symbols of the given number of steps.

Parameters:

  • steps (int) – the number of steps.

  • initial_state (Optional[Union [int, str]]) – the initial state (if omitted, it is chosen uniformly at random).

  • final_state (Optional[Union [int, str]]) – the final state of the simulation (if specified, the simulation stops as soon as it is reached even if not all the steps have been performed).

  • final_symbol (Optional[Union [int, str]]) – the final state of the simulation (if specified, the simulation stops as soon as it is reached even if not all the steps have been performed).

  • output_indices (bool) – a boolean indicating whether to output the state indices.

  • seed (Optional[int]) – a seed to be used as RNG initializer for reproducibility purposes.

Raises:

ValidationError – if any input argument is not compliant.

Return Type:

Union[Tuple[List[int], List[int]], Tuple[List[str], List[str]]]

to_dictionary()[source]

The method returns a dictionary representing the hidden Markov model.

Return Type:

Dict[Tuple[str, str, str], float]

to_file(file_path)[source]

The method writes a hidden Markov model to the given file.

Only csv, json, txt and xml files are supported; data format is inferred from the file extension.
Parameters:

file_path (Union[str, Path]) – the location of the file in which the hidden Markov model must be written.

Raises:
to_graph()[source]

The method returns a directed graph representing the hidden Markov model.

Return Type:

DiGraph

to_matrices()[source]

The method returns a tuple of two items representing the underlying matrices of the hidden Markov model.

The first item is the transition matrix and the second item is the emission matrix.
Return Type:

Tuple[ndarray, ndarray]

transition_probability(state_target, state_origin)[source]

The method computes the probability of a given state, conditioned on the process being at a given state.

Parameters:
Raises:

ValidationError – if any input argument is not compliant.

Return Type:

float