Distributed Submodular Maximization
This addresses the scalability issue for machine learning practitioners dealing with massive datasets, though it is an incremental improvement over centralized methods.
The paper tackles the problem of submodular function maximization in a distributed setting, which is crucial for large-scale machine learning tasks like clustering and kernel machines, by developing a two-stage protocol called GreeDi that achieves performance close to centralized approaches under certain conditions, as demonstrated in experiments on tens of millions of examples.
Many large-scale machine learning problems--clustering, non-parametric learning, kernel machines, etc.--require selecting a small yet representative subset from a large dataset. Such problems can often be reduced to maximizing a submodular set function subject to various constraints. Classical approaches to submodular optimization require centralized access to the full dataset, which is impractical for truly large-scale problems. In this paper, we consider the problem of submodular function maximization in a distributed fashion. We develop a simple, two-stage protocol GreeDi, that is easily implemented using MapReduce style computations. We theoretically analyze our approach, and show that under certain natural conditions, performance close to the centralized approach can be achieved. We begin with monotone submodular maximization subject to a cardinality constraint, and then extend this approach to obtain approximation guarantees for (not necessarily monotone) submodular maximization subject to more general constraints including matroid or knapsack constraints. In our extensive experiments, we demonstrate the effectiveness of our approach on several applications, including sparse Gaussian process inference and exemplar based clustering on tens of millions of examples using Hadoop.