Spectral Clustering as a relaxation of the normalized/ratio cut has become one of the standard graph-based clustering methods. Existing methods for the computation of multiple clusters, corresponding to a balanced k -cut of the graph, are either based on greedy techniques or heuristics which have weak connection to the original motivation of minimizing the normalized cut. In this paper we propose a new tight continuous relaxation for any balanced k -cut problem and show that a related recently proposed relaxation is in most cases loose leading to poor performance in practice. For the optimization of our tight continuous relaxation we propose a new algorithm for the difficult sum-of-ratios minimization problem which achieves monotonic descent. Extensive comparisons show that our method outperforms all existing approaches for ratio cut and other balanced k -cut criteria.

Multi-task learning is a powerful method for solving multiple correlated tasks simultaneously.

Events in an online social network can be categorized roughly into endogenous events, where users just respond to the actions of their neighbors within the network, or exogenous events, where users take actions due to drives external to the network. How much external drive should be provided to each user, such that the network activity can be steered towards a target state? In this paper, we model social events using multivariate Hawkes processes, which can capture both endogenous and exogenous event intensities, and derive a time dependent linear relation between the intensity of exogenous events and the overall network activity. Exploiting this connection, we develop a convex optimization framework for determining the required level of external drive in order for the network to reach a desired activity level. We experimented with event data gathered from Twitter, and show that our method can steer the activity of the network more accurately than alternatives.

First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. The paper proposes a fairer optimization criterion, "regularized maximin", for centralized multi-agent MDPs. The idea, taken from the networking literature is elegant. The authors also propose an iterative optimization method that scales somewhat better than linear programming. The description of the transition model, lines 69-79, seems unnecessarily detailed.

We define a fairness solution criterion for multi-agent decision-making problems, where agents have local interests. This new criterion aims to maximize the worst performance of agents with a consideration on the overall performance. We develop a simple linear programming approach and a more scalable game-theoretic approach for computing an optimal fairness policy. This game-theoretic approach formulates this fairness optimization as a two-player zero-sum game and employs an iterative algorithm for finding a Nash equilibrium, corresponding to an optimal fairness policy.

Hessian of the population risk can have zero eigenvalues.

Designing and discovering new molecules is key for addressing some of world's most pressing