tsseg.algorithms.hdp_hsmm package

HDP-HSMM — Bayesian non-parametric state detection with Gibbs sampling.

Description

HDP-HSMM (Hierarchical Dirichlet Process Hidden Semi-Markov Model) is a non-parametric Bayesian model for time series segmentation that does not require the number of states to be specified in advance. It extends the HMM by modelling arbitrary (non-geometric) state durations through explicit duration distributions.

The generative model:

• A Hierarchical Dirichlet Process draws an infinite discrete distribution over states (truncated at n_max_states). Concentration parameters alpha and gamma control state reuse.

• Each state has Normal-Inverse-Wishart emission parameters, allowing multivariate Gaussian observations with learned mean and covariance.

• Each state has a Negative-Binomial duration distribution (shape dur_alpha, rate dur_beta).

• Inference uses blocked Gibbs sampling over n_iter iterations.

Type: state detection

Supervision: fully unsupervised

Scope: univariate and multivariate

Parameters

Name	Type	Default	Description
alpha	float	6.0	Concentration for the DP prior on transitions.
gamma	float	6.0	Concentration for the top-level DP.
init_state_concentration	float	6.0	Concentration for the initial state distribution.
n_iter	int	200	Number of Gibbs sampling iterations.
n_max_states	int	20	Truncation level (max states).
trunc	int	100	Truncation level for duration distributions.
kappa0	float	0.25	Prior strength for NIW.
nu0	float / None	None	Degrees of freedom for NIW (default: obs_dim + 2).
prior_mean	float / array	0.0	Prior mean for emissions.
prior_scale	float / array	1.0	Scale matrix for NIW.
dur_alpha	float	2.0	Shape for duration Gamma prior.
dur_beta	float	0.1	Rate for duration Gamma prior.
axis	int	0	Time axis.

Usage

from tsseg.algorithms import HdpHsmmDetector

detector = HdpHsmmDetector(n_iter=200, n_max_states=10)
states = detector.fit_predict(X)

Implementation: Pure NumPy/SciPy Gibbs sampler. Origin: new code. Replaces the earlier pyhsmm-backed implementation.

Reference: Johnson & Willsky (2013), Bayesian Nonparametric Hidden Semi-Markov Models, JMLR; Nagano, Nakamura, Nagai, Mochihashi, Kobayashi & Kaneko (2019), Sequence Pattern Extraction by Segmenting Time Series Data Using GP-HSMM with HDP, IEEE RA-L.

Submodules

tsseg.algorithms.hdp_hsmm.detector module

Module contents