# A Unified Deep Model of Learning from both Data and Queries for Cardinality Estimation

arXiv: https://arxiv.org/abs/2107.12295 · HTML: https://mlsanity.com/paper/2107.12295/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 76 references that are in the map.
- First posted on arXiv 26 Jul 2021.

## Builds on (most cited first, 19 of 19)

- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [Deep Learning in Neural Networks: An Overview](https://mlsanity.com/paper/1404.7828/) (2014)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [PixelCNN++: Improving the PixelCNN with Discretized Logistic Mixture Likelihood and Other Modifications](https://mlsanity.com/paper/1701.05517/) (2017)
- [MADE: Masked Autoencoder for Distribution Estimation](https://mlsanity.com/paper/1502.03509/) (2015)
- [Learned Cardinalities: Estimating Correlated Joins with Deep Learning](https://mlsanity.com/paper/1809.00677/) (2018)
- [An End-to-End Learning-based Cost Estimator](https://mlsanity.com/paper/1906.02560/) (2019)
- [MuProp: Unbiased Backpropagation for Stochastic Neural Networks](https://mlsanity.com/paper/1511.05176/) (2015)
- [Deep Unsupervised Cardinality Estimation](https://mlsanity.com/paper/1905.04278/) (2019)
- [Autoregressive Energy Machines](https://mlsanity.com/paper/1904.05626/) (2019)
- [NeuroCard: One Cardinality Estimator for All Tables](https://mlsanity.com/paper/2006.08109/) (2020)
- [DeepDB: Learn from Data, not from Queries!](https://mlsanity.com/paper/1909.00607/) (2019)
- [QuickSel: Quick Selectivity Learning with Mixture Models](https://mlsanity.com/paper/1812.10568/) (2018)
- [An Empirical Analysis of Deep Learning for Cardinality Estimation](https://mlsanity.com/paper/1905.06425/) (2019)
- [Improved Cardinality Estimation by Learning Queries Containment Rates](https://mlsanity.com/paper/1908.07723/) (2019)
- [Variable Skipping for Autoregressive Range Density Estimation](https://mlsanity.com/paper/2007.05572/) (2020)
- [Joins on Samples: A Theoretical Guide for Practitioners](https://mlsanity.com/paper/1912.03443/) (2019)

## Built on by (most cited first, 21 of 21)

- [Cardinality Estimation in DBMS: A Comprehensive Benchmark Evaluation](https://mlsanity.com/paper/2109.05877/) (2021)
- [FactorJoin: A New Cardinality Estimation Framework for Join Queries](https://mlsanity.com/paper/2212.05526/) (2022)
- [PRICE: A Pretrained Model for Cross-Database Cardinality Estimation](https://mlsanity.com/paper/2406.01027/) (2024)
- [Theoretical Analysis of Learned Database Operations under Distribution Shift through Distribution Learnability](https://mlsanity.com/paper/2411.06241/) (2024)
- [Duet: efficient and scalable hybriD neUral rElation undersTanding](https://mlsanity.com/paper/2307.13494/) (2023)
- [Cardinality Estimation on Hyper-relational Knowledge Graphs](https://mlsanity.com/paper/2405.15231/) (2024)
- [A Practical Theory of Generalization in Selectivity Learning](https://mlsanity.com/paper/2409.07014/) (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)
- [DistJoin: A Decoupled Join Cardinality Estimator based on Adaptive Neural Predicate Modulation](https://mlsanity.com/paper/2503.08994/) (2025)
- [Data-Agnostic Cardinality Learning from Imperfect Workloads](https://mlsanity.com/paper/2506.16007/) (2025)
- [BitE : Accelerating Learned Query Optimization in a Mixed-Workload Environment](https://mlsanity.com/paper/2306.00845/) (2023)
- [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)
- [BQSched: A Non-intrusive Scheduler for Batch Concurrent Queries via Reinforcement Learning](https://mlsanity.com/paper/2504.19142/) (2025)
- [Sketched Sum-Product Networks for Joins](https://mlsanity.com/paper/2506.14034/) (2025)
- [A Lightweight Learned Cardinality Estimation Model](https://mlsanity.com/paper/2508.09602/) (2025)
- [QCardEst/QCardCorr: Quantum Cardinality Estimation and Correction](https://mlsanity.com/paper/2509.08817/) (2025)
- [ZeroCard: Cardinality Estimation with Zero Dependence on Target Databases -- No Data, No Query, No Retraining](https://mlsanity.com/paper/2510.07983/) (2025)
- [CoLSE: A Lightweight and Robust Hybrid Learned Model for Single-Table Cardinality Estimation using Joint CDF](https://mlsanity.com/paper/2512.12624/) (2025)
- [TiCard: Deployable EXPLAIN-only Residual Learning for Cardinality Estimation](https://mlsanity.com/paper/2512.14358/) (2025)

## Abstract (arXiv)

Cardinality estimation is a fundamental problem in database systems. To capture the rich joint data distributions of a relational table, most of the existing work either uses data as unsupervised information or uses query workload as supervised information. Very little work has been done to use both types of information, and cannot fully make use of both types of information to learn the joint data distribution. In this work, we aim to close the gap between data-driven and query-driven methods by proposing a new unified deep autoregressive model, UAE, that learns the joint data distribution from both the data and query workload. First, to enable using the supervised query information in the deep autoregressive model, we develop differentiable progressive sampling using the Gumbel-Softmax trick. Second, UAE is able to utilize both types of information to learn the joint data distribution in a single model. Comprehensive experimental results demonstrate that UAE achieves single-digit multiplicative error at tail, better accuracies over state-of-the-art methods, and is both space and time efficient.