The manuscript "Learning Concave Conditional Likelihood Models for Improved Analysis of Tandem Mass Spectra" extends a dynamic Bayesian network approach called DIDEA by introducing a new class of emission distributions. The conditional log-likelihood of those functions remains concave leading to an efficient global optimization method for parameter estimation. This is in stark contrast to the previous variant, for which the best parameter had to be found by grid search. In comparison to other state-of-the-art methods, the new approach outperforms the other methods, while being faster at the same time. Quality Overall the quality of the manuscript is good.

This paper is very interesting. One previous assumption in TD learning is that reward are close with states in proximity of the state space, which has been pointed out by many papers is not realistic and have problems for spatial value function regularization. Instead, this paper make the assumption that rewards are close for states. Overall this paper has a very good motivation, and the literature review shows that the author is knowledgable of this field. This paper could open a novel area of temporal regularization that received inadequate attention before.

I preface this by saying that I have reviewed this paper once for NIPS 2016, and re-read it. It seems the paper has no essential changes, so my opinion is largely the same. The paper considers the problem of learning the parameters of a Bayes net with known structure, given samples from it with potentially adversarial noise. The main goal is to get bounds on the samples that are independent of dimension. The main requirements on the Bayes net parameters are reasonable: the probability of any configuration of the parents is reasonable and the conditional probabilities on any edge are bounded away from 0 and 1.

This is an excellent theoretical contribution. The analysis is quite heavy and has many subtleties. I do not have enough time to read the appended proofs; also, the subject of the paper is not in my area of research. The comments below are based on the impression I got after reading carefully the first 8 pages of the paper and glancing through the rest in the supplementary file. Summary: This paper is about reinforcement learning in weakly-communicating MDP under the average-reward criterion.

This paper puts forward the idea that we should in certain cases regularize the generative model in VAEs in order to improve generalization properties. Since VAEs perform maximum likelihood estimation, they can in principle exhibit the same overfitting problems as any other maximum likelihood model. This paper argues that we can regularize the generative model by increasing the smoothness of the inference model. The authors consider the Denoising VAE (DVAE) as a means of achieving such regularization. In the special case where the encoder is an exponential family, they show that the optimum natural parameters for any input data can be expressed as a weighted average over the optimum parameters for the data in the training set.

POST REBUTTAL: I do think that the edit to the proof suggested by the authors could work, but would lead to some exorbitant constant C4, a subject not addressed by the authors. Still, I have increased my score from "clear reject" to "accept" in the light of the fact that I am now happy with the validity of the proofs.

This work expands on the algorithm RAI by Yehezkel and Lerner for constraint-based structure learning of Bayesian networks. Each node of the tree splits the variables into subsets (one descendant and K ancestral subsets) by using conditional independence (CI) tests of order n. The submission proposes the B-RAI algorithm that leverages bootstrap to allow the algorithm to output a set of highly likely CPDAG rather than the MAP one. Bootstrap is not naively leveraged. Instead, it is integrated in the recursive call of the algorithm.

This paper formulates a framework which unifies several interactive learning problems with a structure such as interactive clustering. Next, the authors show that QBC can be generalized and kernelized to solve the problems in the framework. The consistency and rate of convergence are analyzed. I do not think I could judge the novelty of the theorems and proofs well. Thus, my comments focus on the practicality of the proposed algorithm, which I believe is relevant to its significance and the impact to the field.

Updated Review after Rebuttal: After reading the authors response and re-evaluate the paper I do agree that most of my concerns that there was a fundamental issue with some of their statements were wrong, hence I'm changing my score from 3 to 6. From going into detail of the proof it resides on constructing a generative model where for half of the latent variables (w t z 0) the integral is bounded for all data points and for the other half for 1 data point the integral diverges while for the other goes to zero. This split allows them to say that the one integral diverges and the all of the others are finite hence the likelihood is infinite. However, I'm still not convinced that this issue actually arises at all in practical settings. First, in practice, we are optimizing an ELBO which is never tight, hence for this to be convincing argument the authors should investigate whether there are settings of the ELBO where it diverges except when it can perfectly reconstruct the posterior. Furthermore, I still stand that I do not think that the results on the Frey Faces dataset are interpreted correctly and given that this is a fairly small dataset it is highly likely that the generative model overfits to the data (but not in the way for the divergence to happen). The experimental section in this direction seems to be a bit weak, nevertheless, the paper is worth being accepted.

Existing diffusion-based methods for inverse problems sample from the posterior using score functions and accept the generated random samples as solutions. In applications that posterior mean is preferred, we have to generate multiple samples from the posterior which is time-consuming. In this work, by analyzing the probability density evolution of the conditional reverse diffusion process, we prove that the posterior mean can be achieved by tracking the mean of each reverse diffusion step. Based on that, we establish a framework termed reverse mean propagation (RMP) that targets the posterior mean directly. We show that RMP can be implemented by solving a variational inference problem, which can be further decomposed as minimizing a reverse KL divergence at each reverse step. We further develop an algorithm that optimizes the reverse KL divergence with natural gradient descent using score functions and propagates the mean at each reverse step. Experiments demonstrate the validity of the theory of our framework and show that our algorithm outperforms state-of-the-art algorithms on reconstruction performance with lower computational complexity in various inverse problems.