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- W2605384476 abstract "Given matrices X;Y e Rn×K and Se RK×K with positive elements, this paper proposes an algorithm fastRG to sample a sparse matrix A with low rank expectation E(A)=XSYT and independent Poisson elements. This allows for quickly sampling from a broad class of stochastic blockmodel graphs (degree-corrected, mixed membership, overlapping) all of which are specific parameterizations of the generalized random product graph model defined in Section 2.2. The basic idea of fastRG is to first sample the number of edges m and then sample each edge. The key insight is that because of the the low rank expectation, it is easy to sample individual edges. The naive element-wise algorithm requires O(n2) operations to generate the n×n adjacency matrix A. In sparse graphs, where m = O(n), ignoring log terms, fastRG runs in time O(n). An implementation in R is available on github. A computational experiment in Section 2.4 simulates graphs up to n = 10;000;000 nodes with m = 100;000;000 edges. For example, on a graph with n = 500;000 and m = 5;000; 000, fastRG runs in less than one second on a 3.5 GHz Intel i5." @default.
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- W2605384476 date "2018-01-01" @default.
- W2605384476 modified "2023-09-28" @default.
- W2605384476 title "A note on quickly sampling a sparse matrix with low rank expectation" @default.
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