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Learning Relational Tabular Data without Shared Features

Zhaomin Wu, Shida Wang, Ziyang Wang, Bingsheng He

TL;DR

This work tackles learning across relational tabular data when tables have no shared features and no pre-aligned samples. It introduces Latent Entity Alignment Learning (Leal), which couples soft alignment with a differentiable cluster sampler to identify and leverage latent correspondences between primary and secondary tables, enabling end-to-end supervised learning. The approach is supported by theoretical results showing that aligned data yield lower loss than misaligned data and that the cluster sampler can approximate any target sampling function; empirical results on five real-world and five synthetic datasets show up to a 26.8% reduction in error over strong baselines, with scalable training thanks to the cluster sampler. Overall, Leal demonstrates a practical path to knowledge fusion across heterogeneous tabular data, with broad implications for domains where data silos impede cross-table learning and integration.

Abstract

Learning relational tabular data has gained significant attention recently, but most studies focus on single tables, overlooking the potential of cross-table learning. Cross-table learning, especially in scenarios where tables lack shared features and pre-aligned data, offers vast opportunities but also introduces substantial challenges. The alignment space is immense, and determining accurate alignments between tables is highly complex. We propose Latent Entity Alignment Learning (Leal), a novel framework enabling effective cross-table training without requiring shared features or pre-aligned data. Leal operates on the principle that properly aligned data yield lower loss than misaligned data, a concept embodied in its soft alignment mechanism. This mechanism is coupled with a differentiable cluster sampler module, ensuring efficient scaling to large relational tables. Furthermore, we provide a theoretical proof of the cluster sampler's approximation capacity. Extensive experiments on five real-world and five synthetic datasets show that Leal achieves up to a 26.8% improvement in predictive performance compared to state-of-the-art methods, demonstrating its effectiveness and scalability.

Learning Relational Tabular Data without Shared Features

TL;DR

This work tackles learning across relational tabular data when tables have no shared features and no pre-aligned samples. It introduces Latent Entity Alignment Learning (Leal), which couples soft alignment with a differentiable cluster sampler to identify and leverage latent correspondences between primary and secondary tables, enabling end-to-end supervised learning. The approach is supported by theoretical results showing that aligned data yield lower loss than misaligned data and that the cluster sampler can approximate any target sampling function; empirical results on five real-world and five synthetic datasets show up to a 26.8% reduction in error over strong baselines, with scalable training thanks to the cluster sampler. Overall, Leal demonstrates a practical path to knowledge fusion across heterogeneous tabular data, with broad implications for domains where data silos impede cross-table learning and integration.

Abstract

Learning relational tabular data has gained significant attention recently, but most studies focus on single tables, overlooking the potential of cross-table learning. Cross-table learning, especially in scenarios where tables lack shared features and pre-aligned data, offers vast opportunities but also introduces substantial challenges. The alignment space is immense, and determining accurate alignments between tables is highly complex. We propose Latent Entity Alignment Learning (Leal), a novel framework enabling effective cross-table training without requiring shared features or pre-aligned data. Leal operates on the principle that properly aligned data yield lower loss than misaligned data, a concept embodied in its soft alignment mechanism. This mechanism is coupled with a differentiable cluster sampler module, ensuring efficient scaling to large relational tables. Furthermore, we provide a theoretical proof of the cluster sampler's approximation capacity. Extensive experiments on five real-world and five synthetic datasets show that Leal achieves up to a 26.8% improvement in predictive performance compared to state-of-the-art methods, demonstrating its effectiveness and scalability.

Paper Structure

This paper contains 29 sections, 4 theorems, 29 equations, 6 figures, 5 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Machine Learning on Tabular Data.
  4. Multi-Modal Learning.
  5. Vertical Federated Learning.
  6. Problem Formulation
  7. Approach
  8. Soft Alignment
  9. Cluster Sampler
  10. Training and Inference
  11. Training.
  12. Inference.
  13. Scalability.
  14. Experiments
  15. Experimental Setup
  16. ...and 14 more sections

Key Result

Theorem 4.1

Let $\mathbf{X}^P\in \mathbb{R}^{n \times m^P}$ and $\mathbf{X}^S\in \mathbb{R}^{n \times m^S}$ be normalized primary and secondary feature matrices, respectively, $\mathbf{y}\in \mathbb{R}^{n}$ be the target variable, and $\mathbf{R}$ be a permutation matrix. For the linear regression model $\mathb

Figures (6)

  • Figure 1: Example of latent alignment learning in a financial application: (left) bank transaction table and (right) Bitcoin transaction table. The tables lack shared features, and the label “Bitcoin-related” can be inferred if bank withdrawals are proportional to Bitcoin deposits (or vice versa).
  • Figure 2: Relationship between data alignment and model training loss. Consider the training of a model on two relational tables: the first table contains a single feature $x_1$ and a binary label $y$, while the second table contains a single feature $x_2$. The left subfigure illustrates the distribution of data points $(x_1, x_2)$ when $x_1$ and $x_2$ are properly aligned, while the right subfigure depicts the case of misaligned data. Both subfigures present the converged mean-squared loss and the decision boundary of linear regression.
  • Figure 3: Overall model structure of Leal
  • Figure 4: Capacity of attention mechanism in soft alignment
  • Figure 5: Effect of cluster size $C$ on performance
  • ...and 1 more figures

Theorems & Definitions (9)

  • Theorem 4.1
  • Theorem 4.2
  • Theorem 1.1
  • proof
  • Definition 1.1: Definition of optimal cluster sampler
  • Remark 1.2
  • Theorem 1.2
  • proof
  • Remark 1.3