Sequential Monte Carlo for Graphical Models
We propose a new framework for how to use sequential Monte Carlo (SMC) algorithms for inference in probabilistic graphical models (PGM). Via a sequential decomposition of the PGM we find a sequence of auxiliary distributions defined on a monotonically increasing sequence of probability spaces. By targeting these auxiliary distributions using SMC we are able to approximate the full joint distribution defined by the PGM. One of the key merits of the SMC sampler is that it provides an unbiased estimate of the partition function of the model. We also show how it can be used within a particle Markov chain Monte Carlo framework in order to construct high-dimensional block-sampling algorithms for general PGMs.
The authors propose a method for applying sequential Monte Carlo (SMC) inference to probabilistic graphical models (PGMs). Specifically, the authors show how SMC can be applied to infer latent variables and estimate the partition function (model evidence, posterior normalisation) when a PGM is represented as a factor graph. The authors also show how SMC inference for PGMs can be used as a kernel in an MCMC sampler (via PMCMC) to perform block sampling of latent variables. Finally, the authors apply their method to several datasets showing that their method can i) accurately estimate the partition function and ii) PMCMC sampling can be used to introduce block resampling moves of latent variables with very low auto-correlation.Using SMC for inference in PGMs is an interesting idea that exploits the fact that SMC inference can be done on fairly arbitrary sequence of distributions, provided that the final distribution in the sequence is the desired target distribution. The authors clearly explain how the factor graph representation of a PGM can be decomposed to define such a sequence of distributions. I found the review of factor graphs well written but lacking in references to more detailed resources. I felt a similar section reviewing SMC inference, independent of the application to PGMs would greatly aid paper. As the paper is written it may be difficult for readers without a fairly detailed knowledge of the SMC literature to access the paper. For example the authors talk about adjustment multipliers and fully adapted samplers in section 3.2. While these are important concepts for building efficient SMC samplers, they are also potentially unnecessary complications when presenting the basic idea of SMC inference in PGMs.The experiment in section 5.1 is sound and demonstrates that the estimates of the partition function generated by SMC are comparable to state of the art methods. I am not satisfied with the results of section 5.2. I found it surprising that the authors were able to include $\theta$ as part of the SMC chain, particularly that the variable would be added first during inference. For the synthetic dataset (Figure 6a) the authors show that the SMC algorithm performs reasonably well. I suspect this is due to the small number of topics and the corresponding small dimension of $\theta$. It would be useful to repeat the experiment with a larger number of topics so that the dimension of $\theta$ is larger and see if performance remains competitive with LRS. It is also not clear how the authors are determining the performance on the real data  (Figures 6b-c); are they comparing against LRS or looking at the variability of estimates?The experiment in section 5.3 explores the use of PMCMC for PGMs. Building PMCMC samplers that can update blocks of latent variables by SMC and parameters by Metropolis-Hastings or Gibss sampling could be very powerful. Unfortunately, I feel the experiment is incomplete. The authors only examine auto-correlation times (Figure 7), but do not show a comparison of time complexity of the iterations for each method, or how accurate the different inference schemes are for a fixed computational budget.A few other small issues- For figures 3 and 6a I am not sure what N on the x-axis refers to.- The sentence "Both methods converges to the true value, however, despite the fact that it uses much fewer computational SMC performs significantly better in terms of estimator variance." on lines 369-371 is grammatically incorrect and confusing.- In supplemental section 1.1 I couldn't find the definition for the functions $\kappa$ or $\mu$. They are defined implicitly as the mean and dispersion of a Von Mise distribution, but it would be useful to explicitly state what they are.