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

In this paper, we develop the first one-pass streaming algorithm for submodular maximization that does not evaluate the entire stream even once. By carefully subsampling each element of the data stream, our algorithm enjoys the tightest approximation guarantees in various settings while having the smallest memory footprint and requiring the lowest number of function evaluations. More specifically, for a monotone submodular function and a p-matchoid constraint, our randomized algorithm achieves a 4p approximation ratio (in expectation) with O(k) memory and O(km/p) queries per element (k is the size of the largest feasible solution and m is the number of matroids used to define the constraint).

In this paper, we develop the first one-pass streaming algorithm for submodular maximization that does not evaluate the entire stream even once. By carefully subsampling each element of the data stream, our algorithm enjoys the tightest approximation guarantees in various settings while having the smallest memory footprint and requiring the lowest number of function evaluations. More specifically, for a monotone submodular function and a p-matchoid constraint, our randomized algorithm achieves a 4p approximation ratio (in expectation) with O(k) memory and O(km/p) queries per element (k is the size of the largest feasible solution and m is the number of matroids used to define the constraint).

In this paper, we propose three online algorithms for submodular maximization.

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

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

In this paper, we propose three online algorithms for submodular maximization.

In this paper, we develop Stochastic Continuous Greedy++ (SCG++), the first efficient variant of a conditional gradient method for maximizing a continuous submodular function subject to a convex constraint.

In many machine learning applications, one needs to interactively select a sequence of items (e.g., recommending movies based on a user's feedback) or make sequential decisions in a certain order (e.g., guiding an agent through a series of states). Not only do sequences already pose a dauntingly large search space, but we must also take into account past observations, as well as the uncertainty of future outcomes. Without further structure, finding an optimal sequence is notoriously challenging, if not completely intractable. In this paper, we view the problem of adaptive and sequential decision making through the lens of submodularity and propose an adaptive greedy policy with strong theoretical guarantees. Additionally, to demonstrate the practical utility of our results, we run experiments on Amazon product recommendation and Wikipedia link prediction tasks.

Most real-world networks are too large to be measured or studied directly and there is substantial interest in estimating global network properties from smaller sub-samples. One of the most important global properties is the number of vertices/nodes in the network. Estimating the number of vertices in a large network is a major challenge in computer science, epidemiology, demography, and intelligence analysis. In this paper we consider a population random graph G = (V, E) from the stochastic block model (SBM) with K communities/blocks. A sample is obtained by randomly choosing a subset W V and letting G(W) be the induced subgraph in G of the vertices in W. In addition to G(W), we observe the total degree of each sampled vertex and its block membership.