mixle.stats.latent.segmental_hidden_markov_model module

Hidden Markov model over arbitrary emission segments.

Each hidden state emits one segment object. The segment can be any data type accepted by that state’s emission distribution: a scalar, tuple, set, sequence, or another composable mixle.stats object. To model variable-length emissions, use a SequenceDistribution (or any other distribution over sequences) as an emission distribution.

Unlike HiddenMarkovModelDistribution, each state keeps its own encoder, so emission distributions may use different distribution classes as long as they can all score the same raw segment observations.

class SegmentalHiddenMarkovModelDistribution(emissions, w=MISSING, transitions=MISSING, len_dist=NullDistribution(), name=None, weights=MISSING, terminal_states=None)

Bases: SequenceEncodableProbabilityDistribution

HMM whose states emit arbitrary segment-valued distributions.

Observations are lists of segment objects. For example, with SequenceDistribution(GaussianDistribution(...), len_dist=...) as an emission, each state emits a variable-length list of real values.

Parameters:

• emissions (Sequence[SequenceEncodableProbabilityDistribution])

• w (Sequence[float] | ndarray)

• transitions (Sequence[Sequence[float]] | ndarray)

• len_dist (SequenceEncodableProbabilityDistribution | None)

• name (str | None)

• weights (Sequence[float] | ndarray)

• terminal_states (set[int] | Sequence[int] | None)

compute_capabilities()

Describe backend support shared by emissions and optional length model.

compute_declaration()

Return a composite compute declaration for the segmental HMM.

property topics: list[SequenceEncodableProbabilityDistribution]

Compatibility alias with HiddenMarkovModelDistribution terminology.

density(x)

Return the probability density or mass at a single observation.

Parameters:

x (Sequence[Any])

Return type:

float

log_density(x)

Return the log-density or log-mass at a single observation.

Parameters:

x (Sequence[Any])

Return type:

float

seq_log_density(x)

Return vectorized log-density values for sequence-encoded observations.

Parameters:

x (tuple[ndarray, ndarray, tuple[Any, ...], Any | None])

Return type:

ndarray

backend_seq_log_density(x, engine)

Engine-neutral segmental-HMM forward scoring for encoded segment sequences.

Parameters:

• x (tuple[ndarray, ndarray, tuple[Any, ...], Any | None])

• engine (Any)

Return type:

Any

sampler(seed=None)

Return a sampler for drawing observations from this distribution.

Parameters:

seed (int | None)

Return type:

SegmentalHiddenMarkovSampler

estimator(pseudo_count=None)

Return an estimator for fitting this distribution from data.

Parameters:

pseudo_count (float | None)

Return type:

SegmentalHiddenMarkovEstimator

dist_to_encoder()

Return the data encoder used by this distribution for vectorized methods.

Return type:

SegmentalHiddenMarkovDataEncoder

enumerator()

Enumerate segment sequences in descending marginal probability order.

The segmental HMM has the standard HMM forward semantics – each position emits one segment from its state’s distribution, scored independently – so it reuses HiddenMarkovModelEnumerator directly via its per-state emission (topics), log_w, log_transitions, and len_dist. Each segment is drawn from the union of the per-state emission supports, so every emission distribution must itself support enumeration (and a length distribution must be modeled).

Return type:

DistributionEnumerator

class SegmentalHiddenMarkovSampler(dist, seed=None)

Bases: DistributionSampler

Draw iid segmental-HMM observations.

Parameters:

• dist (SegmentalHiddenMarkovModelDistribution)

• seed (int | None)

sample(size=None)

Draw one segment sequence, or size iid segment sequences.

Parameters:

size (int | None)

Return type:

list[Any] | list[list[Any]]

class SegmentalHiddenMarkovAccumulator(accumulators, len_accumulator=NullAccumulator(), keys=(None, None, None), name=None)

Bases: SequenceEncodableStatisticAccumulator

Baum-Welch accumulator for segmental HMMs.

Parameters:

• accumulators (Sequence[SequenceEncodableStatisticAccumulator])

• len_accumulator (SequenceEncodableStatisticAccumulator | None)

• keys (tuple[str | None, str | None, str | None] | None)

• name (str | None)

update(x, weight, estimate)

Update sufficient statistics for one observed segment sequence.

Parameters:

• x (Sequence[Any])

• weight (float)

• estimate (SegmentalHiddenMarkovModelDistribution)

Return type:

None

initialize(x, weight, rng)

Randomly initialize sufficient statistics for one segment sequence.

Parameters:

• x (Sequence[Any])

• weight (float)

• rng (RandomState)

Return type:

None

seq_initialize(x, weights, rng)

Randomly initialize state and emission statistics for encoded sequences.

Parameters:

• x (tuple[ndarray, ndarray, tuple[Any, ...], Any | None])

• weights (ndarray)

• rng (RandomState)

Return type:

None

seq_update(x, weights, estimate)

Update encoded-sequence statistics with Baum-Welch posteriors.

Parameters:

• x (tuple[ndarray, ndarray, tuple[Any, ...], Any | None])

• weights (ndarray)

• estimate (SegmentalHiddenMarkovModelDistribution)

Return type:

None

seq_update_engine(x, weights, estimate, engine)

Engine-resident Baum-Welch E-step (numpy or torch).

Reuses hmm_engine_forward_backward over the sequence-contiguous segment encoding, producing the same initial/state/transition/emission statistics as the host seq_update.

combine(suff_stat)

Merge another segmental-HMM sufficient-statistic value.

Parameters:

suff_stat (tuple[int, ndarray, ndarray, ndarray, Sequence[Any], Any | None])

Return type:

SegmentalHiddenMarkovAccumulator

value()

Return transition, emission, and sequence-length sufficient statistics.

Return type:

tuple[int, ndarray, ndarray, ndarray, tuple[Any, …], Any | None]

from_value(x)

Replace this accumulator from serialized sufficient statistics.

Parameters:

x (tuple[int, ndarray, ndarray, ndarray, Sequence[Any], Any | None])

Return type:

SegmentalHiddenMarkovAccumulator

scale(c)

Scale all weight-linear sufficient statistics by c.

Parameters:

c (float)

Return type:

SegmentalHiddenMarkovAccumulator

key_merge(stats_dict)

Merge keyed initial, transition, emission, and length statistics.

Parameters:

stats_dict (dict[str, Any])

Return type:

None

key_replace(stats_dict)

Replace keyed initial, transition, emission, and length statistics.

Parameters:

stats_dict (dict[str, Any])

Return type:

None

acc_to_encoder()

Return an encoder compatible with the emission and length accumulators.

Return type:

SegmentalHiddenMarkovDataEncoder

class SegmentalHiddenMarkovAccumulatorFactory(factories, len_factory=NullAccumulatorFactory(), keys=(None, None, None), name=None)

Bases: StatisticAccumulatorFactory

Factory for SegmentalHiddenMarkovAccumulator.

Parameters:

• factories (Sequence[StatisticAccumulatorFactory])

• len_factory (StatisticAccumulatorFactory | None)

• keys (tuple[str | None, str | None, str | None] | None)

• name (str | None)

make()

Create a fresh segmental-HMM accumulator.

Return type:

SegmentalHiddenMarkovAccumulator

class SegmentalHiddenMarkovEstimator(estimators, len_estimator=NullEstimator(), pseudo_count=(None, None), name=None, keys=(None, None, None), terminal_states=None)

Bases: ParameterEstimator

Baum-Welch estimator for SegmentalHiddenMarkovModelDistribution.

Parameters:

• estimators (Sequence[ParameterEstimator])

• len_estimator (ParameterEstimator | None)

• pseudo_count (tuple[float | None, float | None] | None)

• name (str | None)

• keys (tuple[str | None, str | None, str | None] | None)

• terminal_states (set[int] | Sequence[int] | None)

accumulator_factory()

Return an accumulator factory for Baum-Welch sufficient statistics.

Return type:

SegmentalHiddenMarkovAccumulatorFactory

estimate(nobs, suff_stat)

Estimate initial, transition, emission, and length distributions.

Parameters:

• nobs (float | None)

• suff_stat (tuple[int, ndarray, ndarray, ndarray, Sequence[Any], Any | None])

Return type:

SegmentalHiddenMarkovModelDistribution

class SegmentalHiddenMarkovDataEncoder(emission_encoders, len_encoder=NullDataEncoder())

Bases: DataSequenceEncoder

Encode a batch of segment sequences for a segmental HMM.

Parameters:

• emission_encoders (Sequence[DataSequenceEncoder])

• len_encoder (DataSequenceEncoder | None)

seq_encode(x)

Flatten segment sequences and encode them for every state emission.

Parameters:

x (Sequence[Sequence[Any]])

Return type:

tuple[ndarray, ndarray, tuple[Any, …], Any | None]

SegmentalHiddenMarkovDistribution

alias of SegmentalHiddenMarkovModelDistribution

SegmentalHiddenMarkovModelAccumulator

alias of SegmentalHiddenMarkovAccumulator

SegmentalHiddenMarkovModelAccumulatorFactory

alias of SegmentalHiddenMarkovAccumulatorFactory

SegmentalHiddenMarkovModelDataEncoder

alias of SegmentalHiddenMarkovDataEncoder

SegmentalHiddenMarkovModelEstimator

alias of SegmentalHiddenMarkovEstimator

SegmentalHiddenMarkovModelSampler

alias of SegmentalHiddenMarkovSampler