fit_mhmm()

fit_mhmm() estimates Mixture HMM parameters with EM. The E-step computes posterior cluster responsibilities; the M-step updates mixture weights and each cluster's HMM parameters.

Function Usage

fit_mhmm(
    model,
    n_iter=100,
    tol=1e-2,
    verbose=False,
    compress=None
)

seqHMM Parameter Mapping

Sequenzo	seqHMM
model	mhmm object
n_iter, tol, verbose	fit_model.mhmm EM controls

Entry Parameters

Parameter	Required	Type	Description
model	✓	MHMM	Model from build_mhmm().
n_iter	✗	int	Maximum EM iterations. Default 100.
tol	✗	float	Log-likelihood convergence tolerance. Default 1e-2.
verbose	✗	bool	Print progress. Default False.
compress	✗	bool / None	Optional repeated-pattern compression control passed to the model's fitting method. None uses the model default.

Returns

The same MHMM object, modified in place:

Attribute	Meaning
log_likelihood	Fitted mixture log-likelihood
cluster_probs	Estimated mixture weights
clusters[k].*	Fitted parameters for cluster k
n_iter, converged	Optimization diagnostics

Example

from sequenzo import SequenceData, load_dataset
from sequenzo.seqhmm import build_mhmm, fit_mhmm, predict_mhmm

df = load_dataset("mvad")
time_cols = list(df.columns[14:])
states = ["employment", "FE", "HE", "joblessness", "school", "training"]
seq = SequenceData(df, time=time_cols, states=states)

mhmm = build_mhmm(seq, n_clusters=3, n_states=4, random_state=42)
mhmm = fit_mhmm(mhmm, n_iter=100, tol=1e-2, verbose=True)

print(mhmm.log_likelihood, mhmm.cluster_probs)
clusters = predict_mhmm(mhmm)

R Counterpart

• Closest R function: seqHMM fit_model() for mhmm objects
• Mapping note: Same EM structure; R may combine with global/local refinement via fit_model_advanced() in Sequenzo.

Notes

• Cluster labels from EM can be label-switching sensitive across runs; compare solutions with BIC and interpret cluster-specific parameters, not just index order.
• Use compare_models() to choose n_clusters and n_states.

See Also

• Markov Chain Models Introduction maps the full HMM-family workflow.
• Model Comparison helps choose between fitted models.
• Sequenzo and seqHMM Mapping gives the R correspondence.

Authors

Code: Yuqi Liang

Documentation: Yuqi Liang

References

Helske, S., & Helske, J. (2019). Mixture hidden Markov models for sequence data: The seqHMM package in R. Journal of Statistical Software, 88(3), 1–32.