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

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

We develop a scalable, computationally efficient method for the task of energy disaggregation for home appliance monitoring. In this problem the goal is to estimate the energy consumption of each appliance over time based on the total energy-consumption signal of a household. The current state of the art is to model the problem as inference in factorial HMMs, and use quadratic programming to find an approximate solution to the resulting quadratic integer program. Here we take a more principled approach, better suited to integer programming problems, and find an approximate optimum by combining convex semidefinite relaxations randomized rounding, as well as a scalable ADMM method that exploits the special structure of the resulting semidefinite program. Simulation results both in synthetic and real-world datasets demonstrate the superiority of our method.

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

We study the cost function for hierarchical clusterings introduced by [16] where hierarchies are treated as first-class objects rather than deriving their cost from projections into flat clusters. It was also shown in [16] that a top-down algorithm returns a hierarchical clustering of cost at most O(αnlog n) times the cost of the optimal hierarchical clustering, where αn is the approximation ratio of the Sparsest Cut subroutine used. Thus using the best known approximation algorithm for Sparsest Cut due to Arora-Rao-Vazirani, the top-down algorithm returns a hierarchical clustering of cost at most O log3/2 ntimes the cost of the optimal solution. We improve this by giving an O(log n)-approximation algorithm for this problem. Our main technical ingredients are a combinatorial characterization of ultrametrics induced by this cost function, deriving an Integer Linear Programming (ILP) formulation for this family of ultrametrics, and showing how to iteratively round an LP relaxation of this formulation by using the idea of sphere growing which has been extensively used in the context of graph partitioning. We also prove that our algorithm returns an O(log n)-approximate hierarchical clustering for a generalization of this cost function also studied in [16]. We also give constant factor inapproximability results for this problem.

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

The amount of data available in the world is growing faster than our ability to deal with it. However, if we take advantage of the internal structure, data may become much smaller for machine learning purposes. In this paper we focus on one of the fundamental machine learning tasks, empirical risk minimization (ERM), and provide faster algorithms with the help from the clustering structure of the data. We introduce a simple notion of raw clustering that can be efficiently computed from the data, and propose two algorithms based on clustering information. Our accelerated algorithm ClusterACDM is built on a novel Haar transformation applied to the dual space of the ERM problem, and our variance-reduction based algorithm ClusterSVRG introduces a new gradient estimator using clustering. Our algorithms outperform their classical counterparts ACDM and SVRG respectively.

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

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

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