First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. Summary of the paper: The paper studies the incremental clustering problem and shows several properties: - It shows that no deterministic memory-bounded incremental clustering method is nice-detecting. Specifically, the authors show that no deterministic nice-detecting incremental clustering algorithm can use less than 2^{cp-1} bits of memory for data in R^p under the l2 metric. Then some example algorithms are displayed. General comments: - The paper is written clearly and the guarantees in this paper are solid.

Many previous approaches have attempted to estimate functional connectivity between neurons using statistical modeling of observational data, but these approaches rely heavily on parametric assumptions and are purely correlational. Recently, however, holographic photostimulation techniques have made it possible to precisely target selected ensembles of neurons, offering the possibility of establishing direct causal links.

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

Finally, based on inlier priority, we propose the negative entropy based score as a simple and effective outlierness measure.

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

SOSNet [47] shows that second-order constraints further improve the descriptors.

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

Nonconvex-concave min-max problem arises in many machine learning applications including minimizing a pointwise maximum of a set of nonconvex functions and robust adversarial training of neural networks. A popular approach to solve this problem is the gradient descent-ascent (GDA) algorithm which unfortunately can exhibit oscillation in case of nonconvexity. In this paper, we introduce a "smoothing" scheme which can be combined with GDA to stabilize the oscillation and ensure convergence to a stationary solution.

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

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.