nucleation

LIT-1622: Beam Sampling for the Infinite Hidden Markov Model

1 min read

Properties5
StatusActive — read 2026-10-27 (NOTE-1204) in full, from the authors' own copy of the ICML paper; worth reading for the beam sampler, which adds a uniform slice variable under each transition so that only finitely many state trajectories of the infinite HMM have positive probability, and then samples a whole trajectory exactly by forward filtering, backward sampling (THEORY-1037). The infinite factorial HMM's inference is built on it. Read it knowing that its case for faster mixing than Gibbs sampling rests on charts, synthetic data and one changepoint series judged by eye (THEORY-1044), and that one of its fixed hyperparameter settings was chosen from the samplers' own results.
Version2
Tagsprobabilistic-modeling, mathematical-statistics
Cited as “paper” byNOTE-1204 — Van Gael, Saatci, Teh and Ghahramani — Beam sampling for the infinite hidden Markov model
Cited as “source” byTHEORY-1037 — In the infinite hidden Markov model, drawing at each time step a slice variable uniformly below the probability of the transition taken leaves the posterior unchanged and leaves only finitely many state trajectories with positive probability, so a whole trajectory can be resampled exactly by forward filtering and backward sampling, with no truncation of the state space, THEORY-1044 — For the infinite hidden Markov model the beam sampler reaches the posterior in fewer iterations than the single-site Gibbs sampler, and is less sensitive to initialization and hyperpriors, particularly when hidden states persist and emissions are uninformative, at a cost per iteration close to the Gibbs sampler's

Graph View

Van Gael, J., Saatci, Y., Teh, Y. W. & Ghahramani, Z. (2008). Beam sampling for the infinite hidden Markov model. In Proceedings of the 25th International Conference on Machine Learning (ICML ‘08), pp. 1088–1095. ACM. doi:10.1145/1390156.1390293.

Read in full on 2026-10-27 (NOTE-1204). Two accounts were drawn from it: THEORY-1037 and THEORY-1044.

Why this is here

The owner asked on 2026-10-27 to “file the next readings”. The infinite factorial HMM (LIT-1577) samples each of its binary chains with a slice variable and forward filtering, backward sampling, the scheme introduced here for the infinite HMM. The record held the Markov IBP’s prior and not the inference that makes it usable; any fitting of a dynamic feature model such as CASE-165’s would need a sampler of this kind for its per-feature chains.

Backlinks