## Abstract

We consider the problem of estimating the number of distinct elements in a large data set (or, equivalently, the support size of the distribution induced by the data set) from a random sample of its elements. The problem occurs in many applications, including biology, genomics, computer systems and linguistics. A line of research spanning the last decade resulted in algorithms that estimate the support up to ±εn from a sample of size O(log^{2}(1/ε) · n/log n), where n is the data set size. Unfortunately, this bound is known to be tight, limiting further improvements to the complexity of this problem. In this paper we consider estimation algorithms augmented with a machine-learning-based predictor that, given any element, returns an estimation of its frequency. We show that if the predictor is correct up to a constant approximation factor, then the sample complexity can be reduced significantly, to log(1/ε) · n^{1−Θ(1}/log(1/ε)). We evaluate the proposed algorithms on a collection of data sets, using the neural-network based estimators from Hsu et al, ICLR'19 as predictors. Our experiments demonstrate substantial (up to 3x) improvements in the estimation accuracy compared to the state of the art algorithm.

Original language | English |
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State | Published - 2021 |

Externally published | Yes |

Event | 9th International Conference on Learning Representations, ICLR 2021 - Virtual, Online Duration: 3 May 2021 → 7 May 2021 |

### Conference

Conference | 9th International Conference on Learning Representations, ICLR 2021 |
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City | Virtual, Online |

Period | 3/05/21 → 7/05/21 |

### Bibliographical note

Publisher Copyright:© 2021 ICLR 2021 - 9th International Conference on Learning Representations. All rights reserved.