First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. This paper develops a model for multifurcating trees with edge lengths and observed data at the tree leaves; the model is based on the beta coalescent from the probability literature. The authors develop an MCMC inference scheme for their model, in which they draw on existing work that uses belief propagation to perform inference for the Kingman coalescent (an edge case of the beta coalescent in which all trees are binary). The particular challenge for inference here is that there are many more possible parent-child node relationships when parents can have multiple children (not just two). The authors seem to use a Dirichlet Process mixture model (DPMM) at each node to narrow down the space of possible children subsets to consider. As the authors note, even inference with the Kingman coalescent is a hard problem. In experiments, they compare to the Kingman coalescent and hierarchical agglomerative clustering. The Kingman coalescent is a popular modeling tool, so it is great to see a practical extension of the Kingman coalescent to the multifurcating case being explored for inference.

Our goal is to provide efficient algorithms to discover bushy hierarchies.

However, both steps suffer from high computational and memory complexity, preventing the application of SSC to large-scale datasets.

We consider the problem of identifying multiway block structure from a large noisy tensor. Such problems arise frequently in applications such as genomics, recommendation system, topic modeling, and sensor network localization.

We thank the reviewers for the helpful comments and feedback. Our responses are detailed below. We will make the suggested edits for clarity. The improved interpretability with little loss of accuracy makes the sparse TBM appealing in applications. We agree with reviewer that MSE is not the best metric for clustering.

First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. The authors study a variant of ratio cut with R clusters where the balancing function is biased towards partitions where each cluster has the same size. The main contribution of the paper is a continuous formulation and an algorithm to optimize the criterion directly, whereas previous algorithms are mostly limited to recursive splitting. The direct solution of multi-cut problems instead of using recursive splitting is an important problem given the new developments in finding balanced graph cuts [3,4,5,11,12,18]. The authors first describe the discrete problem (P) and then derive a relaxation of the problem (P-rlx).

Fortunately, in many realistic scenarios, only a handful of features may be relevant in distinguishing clusters.

First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. This paper presents an unsupervised dimensionality reduction algorithm which is based on the information bottleneck (IB) method. The method optimizes a constrained objective which, like the IB method, is comprised of the mutual information criteria. The criteria are between a joint density of discrete observed variables and the densities of a set of discrete latent factors, and between factored densities of the observed variables and the latent factors' densities. The goal of the the objective function is to infer latent factors such that by conditioning on them, the observed variables can be factorized into subsets of minimally correlated elements.