# Deep Unsupervised Cardinality Estimation

## TL;DR

This paper introduces a deep autoregressive model-based estimator for cardinality estimation that efficiently handles high-dimensional range queries, significantly improving accuracy over existing methods without relying on independence assumptions.

## Contribution

It develops a Monte Carlo integration scheme for deep autoregressive models to produce a practical, high-accuracy cardinality estimator for complex multi-dimensional queries.

## Key findings

- Achieves single-digit multiplicative error at tail
- Up to 90× accuracy improvement over second best
- Space- and runtime-efficient implementation

## Abstract

Cardinality estimation has long been grounded in statistical tools for density estimation. To capture the rich multivariate distributions of relational tables, we propose the use of a new type of high-capacity statistical model: deep autoregressive models. However, direct application of these models leads to a limited estimator that is prohibitively expensive to evaluate for range or wildcard predicates. To produce a truly usable estimator, we develop a Monte Carlo integration scheme on top of autoregressive models that can efficiently handle range queries with dozens of dimensions or more. Like classical synopses, our estimator summarizes the data without supervision. Unlike previous solutions, we approximate the joint data distribution without any independence assumptions. Evaluated on real-world datasets and compared against real systems and dominant families of techniques, our estimator achieves single-digit multiplicative error at tail, an up to 90$\times$ accuracy improvement over the second best method, and is space- and runtime-efficient.