So, informally speaking, there is a duality between approximation factors of parallel rounding and multiplicative bounds of move-making. This duality is also invariant to applying the rounding on an interval of labels, or over a hierarchical clustering of labels.

First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. The authors present a flexible variational inference method geared Gaussian process models with various likelihoods. Specifically, they derive an inference method for models where some fixed number of latent functions (with GP priors that depend on the input covariate) parameterize a likelihood for conditionally independent observations. They use variational inference to obtain the posterior over the latent functions, where the variational family of distributions is taken to be a mixture of Gaussians with some fixed number of components, and some covariance complexity (full, diagonal, block diagonal, etc). The paper derives the standard evidence lower bound (ELBO), which decomposes into a negative KL term and an expected log-likelihood term, and they note some convenient properties of these decompositions (re: optimizing covariance function parameters). This paper is well written, very clear, and technically sound.

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/

We study a wide class of non-convex non-concave min-max games that generalizes over standard bilinear zero-sum games.

In this work, we generalize the notion of a von Neumann winner to the multi-criteria setting by taking inspiration from Blackwell's approachability.

We consider the problem of minimizing block-separable (non-smooth) convex functions subject to linear constraints. While the Alternating Direction Method of Multipliers (ADMM) for two-block linear constraints has been intensively studied both theoretically and empirically, in spite of some preliminary work, effective generalizations of ADMM to multiple blocks is still unclear. In this paper, we propose a parallel randomized block coordinate method named Parallel Direction Method of Multipliers (PDMM) to solve optimization problems with multi-block linear constraints. At each iteration, PDMM randomly updates some blocks in parallel, behaving like parallel randomized block coordinate descent. We establish the global convergence and the iteration complexity for PDMM with constant step size. We also show that PDMM can do randomized block coordinate descent on overlapping blocks. Experimental results show that PDMM performs better than state-of-the-arts methods in two applications, robust principal component analysis and overlapping group lasso.

We modify the recent convex formulation of the 2-SUM problem introduced by Fogel et al. [2] to use this polytope, and demonstrate how we can attain results of similar quality in significantly less computational time for large n . To our knowledge, this is the first usage of Goemans' compact formulation of the permutahedron in a convex optimization problem. We also introduce a simpler regularization scheme for this convex formulation of the 2-SUM problem that yields good empirical results.