Algorithm reveals causal links despite hidden confounders
Provable Guarantees and Efficient Learning of Structural Equation Models with Latent Confounders
Machine Learning
Summary
Finding cause-and-effect relationships in data is tricky when some factors influencing the results are hidden. The authors present a method to uncover these hidden influences and accurately map out cause-and-effect between observed variables. Their approach breaks down the problem into finding both direct links and the effects of unseen factors, using special mathematical tools. They prove their method works well when enough data is available and confirm it with experiments.
What this means in practice
- •For health data analysts: Identify true causal relationships in patient data while accounting for unmeasured lifestyle or genetic factors.
- •For finance risk modelers: Improve risk assessments by modeling hidden market factors affecting observed financial indicators.
Authors
Weijian Yu, Jean Honorio
Abstract
Causal discovery aims to recover causal relationships from observed data. In various fields, exploring causal relationships among variables remains an important topic, but this task becomes challenging due to the existence of latent confounders. Ignoring such confounders can lead to false associations and incorrect edge directions. In this paper, we study the linear structural equation model with latent confounders. We propose an algorithm that iteratively identifies terminal (observed) nodes and reconstructs the directed acyclic graph of the observed variables. To do this, we recover the precision matrix of the observed variables as a sparse plus low-rank matrix: a sparse matrix captures the conditional dependencies among observed variables, while a low-rank matrix captures the combined influence of a few latent confounders. We establish that for $p$ observed variables, $r$ latent confounders and $s$ edges, our procedure correctly identifies the directed causal relationship among observed variables, for $n \gtrsim \max\{s\log p,\ r p\}$ samples. Experimental results validate our theoretical contributions.