librosa.sequence.viterbi_binary¶
- librosa.sequence.viterbi_binary(prob, transition, *, p_state=None, p_init=None, return_logp=False)[source]¶
Viterbi decoding from binary (multi-label), discriminative state predictions.
Given a sequence of conditional state predictions
prob[s, t]
, indicating the conditional likelihood of states
being active conditional on observation at timet
, and a 2*2 transition matrixtransition
which encodes the conditional probability of moving from states
to state~s
(not-s
), the Viterbi algorithm computes the most likely sequence of states from the observations.This function differs from
viterbi_discriminative
in that it does not assume the states to be mutually exclusive.viterbi_binary
is implemented by transforming the multi-label decoding problem to a collection of binary Viterbi problems (one for each state or label).The output is a binary matrix
states[s, t]
indicating whether each states
is active at timet
.Like
viterbi_discriminative
, the probabilities of the optimal state sequences are not normalized here. If using the return_logp=True option (see below), be aware that the “probabilities” may not sum to (and may exceed) 1.- Parameters:
- probnp.ndarray [shape=(…, n_steps,) or (…, n_states, n_steps)], non-negative
prob[s, t]
is the probability of states
being active conditional on the observation at timet
. Must be non-negative and less than 1.If
prob
is 1-dimensional, it is expanded to shape(1, n_steps)
.If
prob
contains multiple input channels, then each channel is decoded independently.- transitionnp.ndarray [shape=(2, 2) or (n_states, 2, 2)], non-negative
If 2-dimensional, the same transition matrix is applied to each sub-problem.
transition[0, i]
is the probability of the state going from inactive toi
,transition[1, i]
is the probability of the state going from active toi
. Each row must sum to 1.If 3-dimensional,
transition[s]
is interpreted as the 2x2 transition matrix for state labels
.- p_statenp.ndarray [shape=(n_states,)]
Optional: marginal probability for each state (between [0,1]). If not provided, a uniform distribution (0.5 for each state) is assumed.
- p_initnp.ndarray [shape=(n_states,)]
Optional: initial state distribution. If not provided, it is assumed to be uniform.
- return_logpbool
If
True
, return the (unnormalized) log-likelihood of the state sequences.
- Returns:
- Either
states
or(states, logp)
: - statesnp.ndarray [shape=(…, n_states, n_steps)]
The most likely state sequence.
- logpnp.ndarray [shape=(…, n_states,)]
If
return_logp=True
, the (unnormalized) log probability of each state activation sequencestates
- Either
See also
viterbi
Viterbi decoding from observation likelihoods
viterbi_discriminative
Viterbi decoding for discriminative (mutually exclusive) state predictions
Examples
In this example, we have a sequence of binary state likelihoods that we want to de-noise under the assumption that state changes are relatively uncommon. Positive predictions should only be retained if they persist for multiple steps, and any transient predictions should be considered as errors. This use case arises frequently in problems such as instrument recognition, where state activations tend to be stable over time, but subject to abrupt changes (e.g., when an instrument joins the mix).
We assume that the 0 state has a self-transition probability of 90%, and the 1 state has a self-transition probability of 70%. We assume the marginal and initial probability of either state is 50%.
>>> trans = np.array([[0.9, 0.1], [0.3, 0.7]]) >>> prob = np.array([0.1, 0.7, 0.4, 0.3, 0.8, 0.9, 0.8, 0.2, 0.6, 0.3]) >>> librosa.sequence.viterbi_binary(prob, trans, p_state=0.5, p_init=0.5) array([[0, 0, 0, 0, 1, 1, 1, 0, 0, 0]])