Predicting Switching Graph Labelings with Cluster Specialists

We address the problem of predicting the labeling of a graph in an online setting when the labeling is changing over time. We provide three mistake-bounded algorithms based on three paradigmatic methods for online algorithm design. The algorithm with the strongest guarantee is a quasi-Bayesian classifier which requires $\mathcal{O}(t \log n)$ time to predict at trial $t$ on an $n$-vertex graph. The fastest algorithm (with the weakest guarantee) is based on a specialist [10] approach and surprisingly only requires $\mathcal{O}(\log n)$ time on any trial $t$. We also give an algorithm based on a kernelized Perceptron with an intermediate per-trial time complexity of $\mathcal{O}(n)$ and a mistake bound which is not strictly comparable. Finally, we provide experiments on simulated data comparing these methods.