# Learning Models over Relational Data using Sparse Tensors and Functional Dependencies

arXiv: https://arxiv.org/abs/1703.04780 · HTML: https://mlsanity.com/paper/1703.04780/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Mar 2017.

## Built on by (most cited first, 12 of 12)

- [ARM-Net: Adaptive Relation Modeling Network for Structured Data](https://mlsanity.com/paper/2107.01830/) (2021)
- [Powering In-Database Dynamic Model Slicing for Structured Data Analytics](https://mlsanity.com/paper/2405.00568/) (2024)
- [NeurDB: An AI-powered Autonomous Data System](https://mlsanity.com/paper/2405.03924/) (2024)
- [MEMO: Fine-grained Tensor Management For Ultra-long Context LLM Training](https://mlsanity.com/paper/2407.12117/) (2024)
- [Preserving logical and functional dependencies in synthetic tabular data](https://mlsanity.com/paper/2409.17684/) (2024)
- [Approaching sales forecasting using recurrent neural networks and transformers](https://mlsanity.com/paper/2204.07786/) (2022)
- [Graph Your Own Prompt](https://mlsanity.com/paper/2509.23373/) (2025)
- [Graph Neural Networks on Graph Databases](https://mlsanity.com/paper/2411.11375/) (2024)
- [Compressing Structured Tensor Algebra](https://mlsanity.com/paper/2407.13726/) (2024)
- [Morphing-based Compression for Data-centric ML Pipelines](https://mlsanity.com/paper/2504.11067/) (2025)
- [Closed-Form Steepest Descent Direction toward Flat Minima: Reducing Upper Bounds on the Loss Hessian Eigenspectrum in Neural Networks](https://mlsanity.com/paper/2606.28662/) (2026)
- [InferQ: A Database-Oriented Benchmark for Quantum Circuits Simulation](https://mlsanity.com/paper/2607.29134/) (2026)

## Abstract (arXiv)

Integrated solutions for analytics over relational databases are of great practical importance as they avoid the costly repeated loop data scientists have to deal with on a daily basis: select features from data residing in relational databases using feature extraction queries involving joins, projections, and aggregations; export the training dataset defined by such queries; convert this dataset into the format of an external learning tool; and train the desired model using this tool. These integrated solutions are also a fertile ground of theoretically fundamental and challenging problems at the intersection of relational and statistical data models. This article introduces a unified framework for training and evaluating a class of statistical learning models over relational databases. This class includes ridge linear regression, polynomial regression, factorization machines, and principal component analysis. We show that, by synergizing key tools from database theory such as schema information, query structure, functional dependencies, recent advances in query evaluation algorithms, and from linear algebra such as tensor and matrix operations, one can formulate relational analytics problems and design efficient (query and data) structure-aware algorithms to solve them. This theoretical development informed the design and implementation of the AC/DC system for structure-aware learning. We benchmark the performance of AC/DC against R, MADlib, libFM, and TensorFlow. For typical retail forecasting and advertisement planning applications, AC/DC can learn polynomial regression models and factorization machines with at least the same accuracy as its competitors and up to three orders of magnitude faster than its competitors whenever they do not run out of memory, exceed 24-hour timeout, or encounter internal design limitations.