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librosa.sequence.viterbi

librosa.sequence.viterbi(prob, transition, p_init=None, return_logp=False)

Viterbi decoding from observation likelihoods.

Given a sequence of observation likelihoods prob[s, t], indicating the conditional likelihood of seeing the observation at time t from state s, and a transition matrix transition[i, j] which encodes the conditional probability of moving from state i to state j, the Viterbi algorithm [1] computes the most likely sequence of states from the observations.

[1]

Viterbi, Andrew. “Error bounds for convolutional codes and an asymptotically optimum decoding algorithm.” IEEE transactions on Information Theory 13.2 (1967): 260-269.

Parameters:

probnp.ndarray [shape=(n_states, n_steps), non-negative]

prob[s, t] is the probability of observation at time t being generated by state s.

transitionnp.ndarray [shape=(n_states, n_states), non-negative]

transition[i, j] is the probability of a transition from i->j. Each row must sum to 1.

p_initnp.ndarray [shape=(n_states,)]

Optional: initial state distribution. If not provided, a uniform distribution is assumed.

return_logpbool

If True, return the log-likelihood of the state sequence.

Returns:

Either states or (states, logp):

statesnp.ndarray [shape=(n_steps,)]

The most likely state sequence.

logpscalar [float]

If return_logp=True, the log probability of states given the observations.

See also

viterbi_discriminative

Viterbi decoding from state likelihoods

Examples

Example from https://en.wikipedia.org/wiki/Viterbi_algorithm#Example

In this example, we have two states healthy and fever, with initial probabilities 60% and 40%.

We have three observation possibilities: normal, cold, and dizzy, whose probabilities given each state are:

healthy => {normal: 50%, cold: 40%, dizzy: 10%} and fever => {normal: 10%, cold: 30%, dizzy: 60%}

Finally, we have transition probabilities:

healthy => healthy (70%) and fever => fever (60%).

Over three days, we observe the sequence [normal, cold, dizzy], and wish to know the maximum likelihood assignment of states for the corresponding days, which we compute with the Viterbi algorithm below.

>>> p_init = np.array([0.6, 0.4])
>>> p_emit = np.array([[0.5, 0.4, 0.1],
...                    [0.1, 0.3, 0.6]])
>>> p_trans = np.array([[0.7, 0.3], [0.4, 0.6]])
>>> path, logp = librosa.sequence.viterbi(p_emit, p_trans, p_init,
...                                       return_logp=True)
>>> print(logp, path)
-4.19173690823075 [0 0 1]