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# Space-Efficient Sampling

*Proceedings of the Eleventh International Conference on Artificial Intelligence and Statistics*, PMLR 2:171-178, 2007.

#### Abstract

We consider the problem of estimating nonparametric probability density functions from a sequence of independent samples. The central issue that we address is to what extent this can be achieved with only limited memory. Our main result is a space-efficient learning algorithm for determining the probability density function of a piecewise-linear distribution. However, the primary goal of this paper is to demonstrate the utility of various techniques from the burgeoning field of data stream processing in the context of learning algorithms.