Submitted by Assigned_Reviewer_1 Q1 The authors design and fit a hierarchical Bayesian model for predicting disease trajectories (i.e., a scalar measure of disease severity measured throughout the course of the disease) for individual patients. The overall model is an additive combination of a a number of terms including: (1) a population-level term, (2) a subpopulation term, (3) an individual term, (4) a GP term for structured errors. Each of these terms is a function of time, which is modeled parametrically in terms of the coefficients on pre-defined basis expansions (linear and/or B-splines). The subpopulation term involves a discrete mixture model, and the individual level term is a Bayesian linear regression. Distributions are chosen to be Gaussian, which makes most steps of inference and learning work out nicely.

Belief propagation is a fundamental message-passing algorithm for probabilistic reasoning and inference in graphical models. While it is known to be exact on trees, in most applications belief propagation is run on graphs with cycles. Understanding the behavior of "loopy" belief propagation has been a major challenge for researchers in machine learning and other fields, and positive convergence results for BP are known under strong assumptions which imply the underlying graphical model exhibits decay of correlations. We show, building on previous work of Dembo and Montanari, that under a natural initialization BP converges quickly to the global optimum of the Bethe free energy for Ising models on arbitrary graphs, as long as the Ising model is ferromagnetic (i.e.

In recent years, robust Markov decision processes (MDPs) have emerged as a prominent modeling framework for dynamic decision problems affected by uncertainty.

If you google ``fully adapted particle filters'' you will find a lot more material. The authors have considered four different and all relevant application examples. The experimental section shows that the iFDM seems to work and that it can provide interesting results. The only comparison provided is against the FFBS-type algorithm, which we know will perform worse due to its construction. I know that it is a lot of work to implement other solutions to the problem, but if one were to do so it would probably provide an even better understanding of the performance of the model and it would be interesting to see the performance of existing solution to these problems. For example, for the multitarget tracking example, the simplest solution to this problem would probably be to use an extended Kalman filter together with nearest neighbour data association. Since your targets are very well separated I would expect this solution to perform quite well. It would be interesting to compare your performance against this simple standard solution. I have not worked with the cocktail party problem and the multiuser detection problems, but for the power disaggregation problem there are interesting solutions available, see for example the following NIPS paper (which is gaining some influence): Kolter, J. Z.; Batra, S.; and Ng, A. Y. Energy disaggregation via discriminative sparse coding.

A.3 Other important related works Fundamental sample complexity limits of IL:

The variational bound derived in Song et al.