# Deep Unsupervised Cardinality Estimation

arXiv: https://arxiv.org/abs/1905.04278 · HTML: https://mlsanity.com/paper/1905.04278/

## Key facts

- Cited by 36 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 May 2019.

## Built on by (most cited first, 30 of 36)

- [Cardinality Estimation in DBMS: A Comprehensive Benchmark Evaluation](https://mlsanity.com/paper/2109.05877/) (2021)
- [Lero: A Learning-to-Rank Query Optimizer](https://mlsanity.com/paper/2302.06873/) (2023)
- [A Unified Deep Model of Learning from both Data and Queries for Cardinality Estimation](https://mlsanity.com/paper/2107.12295/) (2021)
- [Balsa: Learning a Query Optimizer Without Expert Demonstrations](https://mlsanity.com/paper/2201.01441/) (2022)
- [A Survey on Advancing the DBMS Query Optimizer: Cardinality Estimation, Cost Model, and Plan Enumeration](https://mlsanity.com/paper/2101.01507/) (2021)
- [FactorJoin: A New Cardinality Estimation Framework for Join Queries](https://mlsanity.com/paper/2212.05526/) (2022)
- [Cortex AISQL: A Production SQL Engine for Unstructured Data](https://mlsanity.com/paper/2511.07663/) (2025)
- [A Unified Transferable Model for ML-Enhanced DBMS](https://mlsanity.com/paper/2105.02418/) (2021)
- [One Model to Rule them All: Towards Zero-Shot Learning for Databases](https://mlsanity.com/paper/2105.00642/) (2021)
- [PRICE: A Pretrained Model for Cross-Database Cardinality Estimation](https://mlsanity.com/paper/2406.01027/) (2024)
- [Towards Foundation Models for Relational Databases [Vision Paper]](https://mlsanity.com/paper/2305.15321/) (2023)
- [Detect, Distill and Update: Learned DB Systems Facing Out of Distribution Data](https://mlsanity.com/paper/2210.05508/) (2022)
- [Theoretical Analysis of Learned Database Operations under Distribution Shift through Distribution Learnability](https://mlsanity.com/paper/2411.06241/) (2024)
- [Kepler: Robust Learning for Faster Parametric Query Optimization](https://mlsanity.com/paper/2306.06798/) (2023)
- [Duet: efficient and scalable hybriD neUral rElation undersTanding](https://mlsanity.com/paper/2307.13494/) (2023)
- [AnnotatedTables: A Large Tabular Dataset with Language Model Annotations](https://mlsanity.com/paper/2406.16349/) (2024)
- [Glue: Adaptively Merging Single Table Cardinality to Estimate Join Query Size](https://mlsanity.com/paper/2112.03458/) (2021)
- [Towards Establishing Guaranteed Error for Learned Database Operations](https://mlsanity.com/paper/2411.06243/) (2024)
- [AI-Driven Research for Databases](https://mlsanity.com/paper/2604.06566/) (2026)
- [Electra: Conditional Generative Model based Predicate-Aware Query Approximation](https://mlsanity.com/paper/2201.12420/) (2022)
- [DistJoin: A Decoupled Join Cardinality Estimator based on Adaptive Neural Predicate Modulation](https://mlsanity.com/paper/2503.08994/) (2025)
- [Fine-Tuning Data Structures for Analytical Query Processing](https://mlsanity.com/paper/2112.13099/) (2021)
- [Baihe: SysML Framework for AI-driven Databases](https://mlsanity.com/paper/2112.14460/) (2021)
- [Multi-agent Databases via Independent Learning](https://mlsanity.com/paper/2205.14323/) (2022)
- [Model Joins: Enabling Analytics Over Joins of Absent Big Tables](https://mlsanity.com/paper/2206.10434/) (2022)
- [Learned k-NN Distance Estimation](https://mlsanity.com/paper/2208.14210/) (2022)
- [BitE : Accelerating Learned Query Optimization in a Mixed-Workload Environment](https://mlsanity.com/paper/2306.00845/) (2023)
- [CONCERTO: Complex Query Execution Mechanism-Aware Learned Cost Estimation](https://mlsanity.com/paper/2412.00749/) (2024)
- [Optimize Cardinality Estimation Model Pretraining by Simplifying the Training Datasets](https://mlsanity.com/paper/2502.14350/) (2025)
- [ACE: A Cardinality Estimator for Set-Valued Queries](https://mlsanity.com/paper/2503.14929/) (2025)

## Abstract (arXiv)

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× accuracy improvement over the second best method, and is space- and runtime-efficient.