Particle Gibbs for Infinite Hidden Markov Models
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.
In this paper the authors makes use of the Particle Gibbs with ancestor sampling algorithm to solve the inference problem in the iHMM. The novelty lies in the application of Particle Gibbs with ancestor sampling via the standard stick-breaking construction for the HDP. The authors also exploits the fact that the model is simple enough to allow for better (i.e. better than the bootstrap) proposal distributions to be used, which is good to see.The paper is well written a pleasant read. As always the degree of novelty can be discussed. In this paper the authors takes an existing inference algorithm (PG with ancestor sampling) and applies it to an existing model (iHMM) in a straightforward manner. This particular combination has not appeared before (as far as I know), so in that sense it is novel, but the ``degree of novelty'' is just that, i.e. applying algorithm X to model Y.As already mentioned above it is good to see that the authors are exploiting the analytical tractability inherent in the model to construct a better proposal distribution. This should always be done when it is possible. If you want more background on this you can consult the literature on the so called ``fully adapted'' particle filter. I think you might be able to adapt also the resampling step for your model. Anyhow, just a thought.A detail: The authors writes (already in the abstract) that ``... leverages ancestor sampling to suppress degeneracy of the standard PG algorithm.'' Technically this is not correct. Note that the PG sampler with ancestor sampling also degenerates, but importantly it (with a very high probability) degenerates to a new trajectory in each iteration. The fact that the algorithm degenerates to a different trajectory in each iteration is indeed what improves the mixing when compared to the original PG sampler.