Learning-based Support Estimation in Sublinear Time
Authors: Talya Eden,Piotr Indyk,Shyam Narayanan,Ronitt Rubinfeld,Sandeep Silwal,Tal Wagner

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 $ \pm \varepsilon n$ from a sample of size $O(\log^2(1/\varepsilon) \cdot n/\log n)$, 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
$$ \ \log (1/\varepsilon) \cdot n^{1-\Theta(1/\log(1/\varepsilon))}. $$
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.