Paper:
VARIATIONAL BAYESIAN PHYLOGENETIC INFERENCE
Bayesian phylogenetic inference is currently done via Markov chain Monte Carlo with simple mechanisms for proposing new states, which hinders exploration efficiency and often requires long runs to deliver accurate posterior estimates. In this paper we present an alternative approach: a variational framework for Bayesian phylogenetic analysis. We approximate the true posterior using an expressive graphical model for tree distributions, called a subsplit Bayesian network, together with appropriate branch length distributions. We train the variational approximation via stochastic gradient ascent and adopt multi-sample based gradient estimators for different latent variables separately to handle the composite latent space of phylogenetic models. We show that our structured variational approximations are flexible enough to provide comparable posterior estimation to MCMC, while requiring less computation due to a more efficient tree exploration mechanism enabled by variational inference. Moreover, the variational approximations can be readily used for further statistical analysis such as marginal likelihood estimation for model comparison via importance sampling. Experiments on both synthetic data and real data Bayesian phylogenetic inference problems demonstrate the effectiveness and efficiency of our methods.

Review:
This paper explores an approximate inference solution to the challenging problem of Bayesian inference of phylogenetic trees. Its leverages recently proposed subsplit Bayesian networks (SBNs) as a variational approximation over tree space and combines this with modern gradient estimators for VI. It is thorough in its evaluation of both methodological considerations and different datasets.
The main advantage would seem to be a large speedup over MCMC-based methods (Figure 4), which could be of significant value to the phylogenetics community. This point would benefit from more discussion. How do the number of iterations (reported in Figures 3&4, which was done carefully) correspond to wallclock time? Can this new method scale to numbers of sites and sequences that were previously unfeasible?
The main technical contribution is the use of SBNs as variational approximations over tree-space, but it is difficult to follow their implementation and parameter sharing without the explanation of the original paper. Additionally, the issue of estimating the support of the subsplit CPTs needs more discussion. As the authors acknowledge, complete parameterizations of these models scale in a combinatorial way with “all possible parent-child subsplit pairs”, and they deal with this by shrinking the support up front with various heuristics. It seems that these support estimation approaches would be feasible when the data are strong but would become challenging to scale when the data are weak. Since VB is often concerned with the limited-data regime, more discussion of when support estimation is feasible and when it is difficult would clarify how widely applicable the method is.
Overall, this work is an interesting extension of variational Bayes to a tree-structured inference problem and is thorough in its evaluation. While it is a bit focused on classical inference for ICLR, it could be interesting both for the VI community and as a significant application advancement.
Other notes:
In table 1, is the point that all methods are basically the same with different variance? This is not clear from the text. What about the variational bounds?