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# Spoofing Large Probability Mass Functions to Improve Sampling Times and Reduce Memory Costs

*Proceedings of the Seventeenth International Conference on Artificial Intelligence and Statistics*, PMLR 33:743-750, 2014.

#### Abstract

Sampling from a probability mass function (PMF) has many applications in modern computing. This paper presents a novel lossy compression method intended for large (O(10^5)) dense PMFs that speeds up the sampling process and guarantees high fidelity sampling. This compression method closely approximates an input PMF P with another PMF Q that is easy to store and sample from. All samples are drawn from Q as opposed to the original input distribution P. We say that Q “spoofs” P while this switch is difficult to detect with a statistical test. The lifetime of Q is the sample size required to detect the switch from P to Q. We show how to compute a single PMF’s lifetime and present numeric examples demonstrating compression rates ranging from 62% to 75% when the input PMF is not sorted and 88% to 99% when the input is already sorted. These examples have speed ups ranging from 1.47 to 2.82 compared to binary search sampling.