A fine-grained look at causal effects in causal spaces

2025-12-11

AI Summary

Traditional causal inference operates at the variable level (e.g., drug dosage → blood pressure), rendering it ill-suited for high-dimensional unstructured data—such as image pixels or text tokens—that lack explicit semantic structure. This paper introduces a novel event-level causal effect paradigm, grounded in a measure-theoretic causal space framework. It axiomatically defines causality existence criteria and a strength quantification system over event algebras—the first such formalization. Methodologically, it establishes a rigorous correspondence between causality under intervention measures and (in)dependence, thereby unifying and reproducing standard treatment effect estimands—including ATE and ATT. Theoretical contributions include: (1) a decidable binary criterion for causal existence; (2) a directional, interpretable metric for causal strength; and (3) a rigorous proof of degeneracy consistency. This work transcends variable-level modeling constraints and provides a foundational framework for causal analysis of high-dimensional unstructured data.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Knowledge Representation and Reasoning: Action, Change, and Causality

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Bridging structured and unstructured data
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

The notion of causal effect is fundamental across many scientific disciplines. Traditionally, quantitative researchers have studied causal effects at the level of variables; for example, how a certain drug dose (W) causally affects a patient's blood pressure (Y). However, in many modern data domains, the raw variables-such as pixels in an image or tokens in a language model-do not have the semantic structure needed to formulate meaningful causal questions. In this paper, we offer a more fine-grained perspective by studying causal effects at the level of events, drawing inspiration from probability theory, where core notions such as independence are first given for events and sigma-algebras, before random variables enter the picture. Within the measure-theoretic framework of causal spaces, a recently introduced axiomatisation of causality, we first introduce several binary definitions that determine whether a causal effect is present, as well as proving some properties of them linking causal effect to (in)dependence under an intervention measure. Further, we provide quantifying measures that capture the strength and nature of causal effects on events, and show that we can recover the common measures of treatment effect as special cases.

Problem

• Develops causal effect definitions for events in causal spaces
• Quantifies strength and nature of causal effects on events
• Generalizes traditional variable-level causal measures to event-level

Innovation

• Causal effects at event level, not variables
• Measure-theoretic framework for causal spaces
• Quantifying strength and nature of causal effects