Finding Structure and Causality in Linear Programs

TL;DR

This paper introduces a causal perspective on Linear Programs, revealing new structural insights and relations within LP components through systematic empirical analysis across various LP types.

Contribution

It provides a foundational causal framework for understanding LPs, which enhances their interpretability and potential applications in machine learning.

Findings

Revealed intra- and inter-structure relations in LP components

Systematic empirical analysis on different LP types

Uncovered new structural insights in LPs

Abstract

Linear Programs (LP) are celebrated widely, particularly so in machine learning where they have allowed for effectively solving probabilistic inference tasks or imposing structure on end-to-end learning systems. Their potential might seem depleted but we propose a foundational, causal perspective that reveals intriguing intra- and inter-structure relations for LP components. We conduct a systematic, empirical investigation on general-, shortest path- and energy system LPs.