First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. In this paper, authors analyze sparsity of the posterior parameters in LDA using a variational Bayesian algorithm. They derive an expression for the VB free energy which shows its asymptotic behaviour with respect to number of words (N), number of documents (M), vocabulary size (L) etc. Their results suggest that, for certain settings of L,M,N, the sparsity behaviour changes drastically at a particular hyper-parameter setting. These changes differ from those of MAP and partial-Bayes algorithms. The problem discussed in this paper is original, interesting, and is perhaps useful too.

First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. This paper proposes the Latent Case Model (LCM), a Bayesian approach to clustering in which clusters are represented by a prototype (a specific sample from the data) and feature subspaces (a binary subset of the variables signifying those features that are relevant to the class). The approach is presented as being a Bayesian, trainable version of the Case-Based Reasoning approach popular in AI, and is motivated by the ways such models have proved highly effective in explaining human decision making. The generative model (Figure 1) represents each item as coming from a mixture of S clusters, where each cluster is represented by a prototype and subspace (as above) and a function \phi which generates features matching those of the prototype with high probability for features in the subspace, and uniform features outside it. The model is thus similar in functionality to LDA but quite different in terms of its representation.

First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. This paper considers weighted majority algorithm and establishes consistency (error rate of the aggregator tending to zero) results under two settings: (1) when the competence level (risk of each expert) is known in advance and (2) when it is estimated. For case (2), frequentist and Bayesian methods for estimating the competence level are provided. For case (1), consistency is established in terms of providing upper and lower bounds on the error rate of the aggregator, which involve standard calculations ( apart from the fact that upper bound is established by invoking a result by Kearns and Saul, instead of Hoeffding's inequality). For case (2) under the frequentist setting, an independent set of labeled inputs is used to estimate the competence level of each expert.

We thank all reviewers for thoughtful feedback! We reply separately to each reviewer. Reviewer #1: We would like to point out some of the paper's main contributions, not fully recognized in the review. Another example is our algorithm for sampling DAGs conditionally on a root-partition (Sections 3.4 Accordingly, our main innovations are algorithmic. We would like to correct that our algorithm for sampling DAGs is not "classical" (cf.

We focus on the case of i.i.d.

We give a tractable unbiased estimate of the log density using a "Russian roulette" estimator, and reduce the memory required