The paper proposes a semidefinite relaxation for K-means clustering with isotropic and non-isotropic mixtures of sub-gaussian distributions in both high and low-dimensions. The paper has a good technical analysis of the methods proposed in it. There are some supporting empirical experiments too. However, one thing would have been useful to see was how computation time scales with both p and n. The empirical experiments considered n 30, which is pretty small for many application situations.

This paper examines the problem of tensor regression and proposes a boosted sparse low-rank model that produces interpretable results. In their low-rank tensor regression model, unit-rank tensors from the CP decomposition of the coefficient tensor is assumed to be sparse. This assumption allows for an interpretable model where the outcome is related to only a subset of features. For model estimation, the authors use a divide-and-conquer strategy to learn the sparse CP decomposition, based on an existing sequential extraction method, where sparse unit-rank problems are sequentially solved. Instead of using an alternating convex search (ACS) approach, the authors use a stage-wise unit-rank tensor factorization algorithm to learn the model.

The paper presents a supervised non-parametric hypothesis transfer learning (HTL) approach for regression and its analysis, aimed at the cases where one has plenty of training data coming from the source task and few examples from the target one. The paper makes an assumption that the source and the target regression functions are related through so called transformation function (TF). The TF is assumed to have some parametric form (e.g. Once these parameters are learned, the hypothesis trained on the source task can be transformed to the hypothesis designated for the target task. The paper proposes two ways for estimation of these parameters, that is through kernel smoothing and kernel ridge regression.

Summary: This work investigates Probabilistic Label Trees (PLTs) in solving extreme multi-label classification (XMLC). The theoretical analysis shows PLT is a no-regret algorithm for precision@k, and the algorithmic improvement combines PLT and fastText to efficiently handle extreme multi-label text classification problems, with a clustering-based tree structure building strategy. This paper is comphrensive and well-written, including extensive experiments. The theory part formally shows PLT outputing k labels with highest marginal probabilities is consistent with precision@k, given zero-regret node classifiers. The authors also provide some negative result on heuristic strategies, one is that pick-one-label heuristic is suboptimal in terms of precision@k, and another is that building Huffman trees for PLT does not minimize computational cost.

Summary The paper proposes an SVM-like classification method for estimating sets containing a pre-specified amount of samples for each class. The overlap of these two sets is a region with ambiguity and should thus be small. The key results are: problem formulation and reformulation using a convex surrogate loss function. Impression The problem formulation is very interesting and the combination of theoretical and experimental results is above standard. In addition, the paper is easy to follow. My main concerns are: - What is the conceptional difference between the proposed approach and classification with reject option as in [2].

The paper proposes a new algorithm for learning node embedding, by bringing together the attention model and the graph likelihood objective function suggested in a recent work [2]. By learning the context distribution determining the coefficients of powers of the transition matrix, it leads to a more flexible representation learning model. Quality: Although the technical content of the paper seems to be correct, I would like to point out some issues in the paper: - In Line 121, the sentence "In practice, random walk methods based on Deepwalk do not use C as a hard limit" is not generally correct because many methods (such as Node2vec) perform fixed length walks. Therefore, I think it could be also better to see its performance against the methods such as HOPE. I would strongly recommend to examine the performance of the method over different training and test sizes.

Supervised dimensionality reduction has become a topic of interest in the systems neuroscience community over the last few years. Here, the authors suggested a very sensible extension to demixed PCA and targeted dimensionality reduction (TDR), which are recently developed but well-known and impactful methods in the field. However, I am disappointed that it heavily relies on simulated data rather than real biological datasets for its results. In particular, all datasets examined by the demixed PCA paper (in eLife) are freely available, so I feel that at least one of those datasets should have been analyzed for the purpose of comparison. I am not convinced that the proposed model would produce qualitatively different results from those already published. That being said, I think the proposed modeling framework is more straightforward than demixed PCA and offers the possibility of interesting future extensions.

Spectral optimization is defined as finding \theta that minimizes F(A(\theta)) g(\theta) where A(\theta) is a symmetric matrix and F typically the trace of an analytic function i.e. F(A) tr(p(A)) where p is a polynomial. They propose an unbiased estimator of F by randomly truncating the Chebyshev approximation to F and doing importance sampling. Moreover, they calculate the optimal distribution for this importance sampling. They demonstrate how this method would be used for SGD and stochastic Variance Reduced Gradient.

The authors proposed a sparse embedded k-means clustering algorithm to improve the running time of matrix multiplication of current proposed randomization projection method under sparse setting of data matrix in the literature. In particular, they demonstrated that their algorithms achieve the calculation time of matrix multiplication of order proportional to the number of non-zeroes entries of data matrix. I think the sparse embedded k-means clustering algorithm is rather interesting; however, it is not a very surprising improvement given the current results from the paper of C. Boutsidis et al. (2015). More specifically, both papers try to approximate low dimension solution for the original solution of K-means problem. To do that, C. Boutsidis et al. (2015) proposed to multiply the data matrix X with a random matrix having entries 1/\sqrt{d'} or -1/\sqrt{d'} where d' is the dimension of the approximation solution.

Summary: This paper presents a new algorithm called Bayesian Distributed SGD to mitigate the straggler problem when training deep learning on parallel clusters. Unlike Synchronous Distributed SGD approach where a fixed cut-off (number of workers) is predefined, BDSGD uses amortized inference to predict workers' run-times and derive a straggler cut-off accordingly. BDSGD models the joint run-time behaviour of workers which are likely to be correlated due to the underlying cluster architecture. The approach is incorporated as part of the parameter server framework, deciding which sub-gradients to drop in each iteration. Strength: The proposed idea of adaptive cut-off and predicting joint worker runtime through amortized inference with variational auto encoder loss is novel and very interesting.