The authors motivate the proposed model with the setting in which items have "true" but unobserved labels/ratings and the observed labels/ratings given by evaluators are potentially incorrect. This differs from the very common problem in recommendation systems or collaborative filtering where evaluators provide their subjective ratings but there is not assumed to be any "true" rating (e.g., users of Netflix giving 1-5 star ratings to movies). This seems like a common but underexplored setting that is worthy of further study within machine learning. The authors are also right to highlight interpretability as a desired aspect of any machine learning solution that may yield post-hoc insights into common human biases and thus suggest corrective measures. This paper does a good job of motivating the proposed model and situating it within the crowdsourcing and human annotation literature.

If my understanding is correct, Theorem 1 of the authors does not quite apply to their algorithm ADD-1/2-Smoothed Low-Rank. Instead, it applies to the non-computable algorithm where they assume that they have a minimizer of the objective function in Theorem 3. It is not clear if the alternating optimization algorithm proposed in the paper is guaranteed to converge to a minimizer of the objective in Theorem 3. If this is true, the authors should mention this before stating Theorem 1 to avoid misleading the reader. The "discounting" seems important from the Experiments section but this is not described in the main paper. If this is so important, the authors should make room for this in the main paper. The main results (Theorem 1 and 2) are not so surprising given that this is almost a parametric estimation problem with mk parameters (so the rates should be km/n).

This is a very good and technically sound paper, containing a significant amount of material. The theoretical investigation of the properties of alpha-divergence minimization is thorough, clear and detailed. The paper provides significant theoretical insight and understanding into alpha-divergence minimization and optimization-based approximate inference in general. My biggest concern about the alpha-divergence framework is whether its theoretical richness and elegance actually translates to practical methods. In other words, I'm not sure that the practical aspects of it are appealing enough to convince practitioners of variational inference to switch to alpha-divergence minimization instead.

The paper is a superbly written account of a simple idea that appears to work very well. The approach can straightforwardly be applied to existing max-likelihood (ML) trained models in order to in principle take into account the task reward during training and is computationally much more efficient than alternative non ML based approaches. This work risks being underappreciated as proposing but a simple addition of artificial structured-label noise, but I think the specific link with structured output task reward is sufficiently original, and the paper also uncovers important theoretical insight by revealing the formal relationship between the proposed reward augmented ML and RL-based regularized expected reward objectives. So while it works surprisingly well, you haven't yet clearly demonstrated empirically that using a truly *task-reward derived* payoff distribution is beneficial. One way to convincingly demonstrate that would be if you did your envisioned BLEU importance reweighted sampling, and were able to show that it improves the BLEU test score over your current simpler edit-distance based label noise.

The paper is very clearly written and describes technical concepts in a very comprehensible way. The approach is sound and well motivated and the experimental comparisons with other approaches are fair, though they could have been more extensive in terms of datasets. My greatest concern is about the execution time of the proposed approach, since this is a sequential Monte Carlo method that performs multiple refinement passes for each step of the training process. The authors report convergence curves vs epochs but not vs wall clock time, which should be provided as the main motivation of the paper is to speed up training for this class of generative methods. The experimental section is good in terms of which methods it compares against, but a bit lacking in terms of datasets.

This is an interesting modeling and model comparison paper, providing insights into the processing of uncertainty during learning and decision making. The paper combines advances that could be interesting to both experimental and modeling audiences. However, its clarity should be improved and parameter estimation details explained much better for the paper to be acceptable to NIPS. More specifically: - Why should highly volatile environments have high learning rates (line 2 of page 2)? Couldn't it plausibly lead to excessive weight instability?

Given ancestral constraints, some pruning of the search tree is possible. Lemma 3 (supplementary material) is the key result here. I believe it to be true, but I don't understand the proof. The phrase "By the EC tree edge generation rules, G_k also contains edge Z - W" needs more explanation. In addition there are implied constraints ( "implied constraints" is the standard terminology, here they are called "projected constraints").

Gaussian graphical models with sparsity in the inverse covariance matrix are of significant interest in many modern applications. For the problem of recovering the graphical structure, information criteria provide useful optimization objectives for algorithms searching through sets of graphs or for selection of tuning parameters of other methods such as the graphical lasso, which is a likelihood penalization technique. In this paper we establish the asymptotic consistency of an extended Bayesian information criterion for Gaussian graphical models in a scenario where both the number of variables p and the sample size n grow. Compared to earlier work on the regression case, our treatment allows for growth in the number of non-zero parameters in the true model, which is necessary in order to cover connected graphs. We demonstrate the performance of this criterion on simulated data when used in conjuction with the graphical lasso, and verify that the criterion indeed performs better than either cross-validation or the ordinary Bayesian information criterion when p and the number of non-zero parameters q both scale with n.

We develop a novel Bayesian nonparametric model for random bipartite graphs. The model is based on the theory of completely random measures and is able to handle a potentially infinite number of nodes. We show that the model has appealing properties and in particular it may exhibit a power-law behavior. We derive a posterior characterization, an Indian Buffet-like generative process for network growth, and a simple and efficient Gibbs sampler for posterior simulation. Our model is shown to be well fitted to several real-world social networks.

Dependent Dirichlet processes (DPs) are dependent sets of random measures, each being marginally Dirichlet process distributed. They are used in Bayesian nonparametric models when the usual exchangebility assumption does not hold. We propose a simple and general framework to construct dependent DPs by marginalizing and normalizing a single gamma process over an extended space. The result is a set of DPs, each located at a point in a space such that neighboring DPs are more dependent. We describe Markov chain Monte Carlo inference, involving the typical Gibbs sampling and three different Metropolis-Hastings proposals to speed up convergence.