Infinite hidden Markov models provide a flexible framework for modelling time series with structural changes and complex dynamics, without requiring the number of latent states to be specified in advance. This flexibility is achieved through the hierarchical Dirichlet process prior, while efficient Bayesian inference is enabled by the beam sampler, which combines dynamic programming with slice sampling to truncate the infinite state space adaptively. Despite extensive methodological developments, the role of initialization in this framework has received limited attention. This study addresses this gap by systematically evaluating initialization strategies commonly used for finite hidden Markov models and assessing their suitability in the infinite setting. Results from both simulated and real datasets show that distance-based clustering initializations consistently outperform model-based and uniform alternatives, the latter being the most widely adopted in the existing literature.

Neural Information Processing Systems http://nips.cc/

Infinite Hidden Markov Models (iHMM's) are an attractive, nonparametric generalization of the classical Hidden Markov Model which can automatically infer the number of hidden states in the system. However, due to the infinite-dimensional nature of the transition dynamics, performing inference in the iHMM is difficult. In this paper, we present an infinite-state Particle Gibbs (PG) algorithm to resample state trajectories for the iHMM. The proposed algorithm uses an efficient proposal optimized for iHMMs and leverages ancestor sampling to improve the mixing of the standard PG algorithm. Our algorithm demonstrates significant convergence improvements on synthetic and real world data sets.

Infinite Hidden Markov Models (iHMM's) are an attractive, nonparametric generalization of the classical Hidden Markov Model which can automatically infer the number of hidden states in the system. However, due to the infinite-dimensional nature of the transition dynamics, performing inference in the iHMM is difficult. In this paper, we present an infinite-state Particle Gibbs (PG) algorithm to resample state trajectories for the iHMM. The proposed algorithm uses an efficient proposal optimized for iHMMs, and leverages ancestor sampling to improve the mixing of the standard PG algorithm. Our algorithm demonstrates significant convergence improvements on synthetic and real world data sets.

Infinite Hidden Markov Models (iHMM's) are an attractive, nonparametric generalization of the classical Hidden Markov Model which can automatically infer the number of hidden states in the system. However, due to the infinite-dimensional nature of transition dynamics performing inference in the iHMM is difficult. In this paper, we present an infinite-state Particle Gibbs (PG) algorithm to resample state trajectories for the iHMM. The proposed algorithm uses an efficient proposal optimized for iHMMs and leverages ancestor sampling to suppress degeneracy of the standard PG algorithm. Our algorithm demonstrates significant convergence improvements on synthetic and real world data sets. Additionally, the infinite-state PG algorithm has linear-time complexity in the number of states in the sampler, while competing methods scale quadratically.

Hidden Markov models (HMMs) are a fundamental tool for data analysis and exploration. Many variants of the basic HMM have been developed in response to shortcomings in the original HMM formulation [9]. In this paper we address inference in the explicit state duration HMM (EDHMM). By state duration we mean the amount of time an HMM dwells in a state. In the standard HMM specification, a state's duration is implicit and, a priori, distributed geometrically. The EDHMM (or, equivalently, the hidden semi-Markov model [12]) was developed to allow explicit parameterization and direct inference of state duration distributions. EDHMM estimation and inference can be performed using the forward-backward algorithm; though only if the sequence is short or a tight "allowable" duration interval for each state is hard-coded a priori [13]. If the sequence is short then forward-backward can be run on a state representation that allows for all possible durations up to the observed sequence length. If the sequence is long then forward-backward only remains computationally tractable if only transitions between durations that lie within pre-specified allowable intervals are considered.