Using Butterfly-Patterned Partial Sums to Optimize GPU Memory Accesses for Drawing from Discrete Distributions

We describe a technique for drawing values from discrete distributions, such as sampling from the random variables of a mixture model, that avoids computing a complete table of partial sums of the relative probabilities. A table of alternate (“butterfly-patterned”) form is faster to compute, making better use of coalesced memory accesses. From this table, complete partial sums are computed on the fly during a binary search. Measurements using an NVIDIA Titan Black GPU show that for a sufficiently large number of clusters or topics (K > 200), this technique alone more than doubles the speed of a latent Dirichlet allocation (LDA) application already highly tuned for GPU execution.