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

We address the problem of predicting the labeling of a graph in an online setting when the labeling is changing over time. We present an algorithm based on a specialist [11] approach; we develop the machinery of cluster specialists which probabilistically exploits the cluster structure in the graph. Our algorithm has two variants, one of which surprisingly only requires O(log n) time on any trial t on an n-vertex graph, an exponential speed up over existing methods. We prove switching mistake-bound guarantees for both variants of our algorithm. Furthermore these mistake bounds smoothly vary with the magnitude of the change between successive labelings. We perform experiments on Chicago Divvy Bicycle Sharing data and show that our algorithms significantly outperform an existing algorithm (a kernelized Perceptron) as well as several natural benchmarks.

We study the problem of completing a binary matrix in an online learning setting. On each trial we predict a matrix entry and then receive the true entry. We propose a Matrix Exponentiated Gradient algorithm [1] to solve this problem. We provide a mistake bound for the algorithm, which scales with the margin complexity [2, 3] of the underlying matrix. The bound suggests an interpretation where each row of the matrix is a prediction task over a finite set of objects, the columns. Using this we show that the algorithm makes a number of mistakes which is comparable up to a logarithmic factor to the number of mistakes made by the Kernel Perceptron with an optimal kernel in hindsight. We discuss applications of the algorithm to predicting as well as the best biclustering and to the problem of predicting the labeling of a graph without knowing the graph in advance.