Towards Computing an Optimal Abstraction for Structural Causal Models

@article{Zennaro2022TowardsCA,
  title={Towards Computing an Optimal Abstraction for Structural Causal Models},
  author={Fabio Massimo Zennaro and Paolo Turrini and Theodoros Damoulas},
  journal={ArXiv},
  year={2022},
  volume={abs/2208.00894}
}
Working with causal models at different levels of abstraction is an important feature of science. Existing work has already considered the problem of expressing formally the relation of abstraction between causal models. In this paper, we focus on the problem of learning abstractions. We start by defining the learning problem formally in terms of the optimization of a standard measure of consistency. We then point out the limitation of this approach, and we suggest extending the objective… 
[PDF] Semantic Reader
1 Citations
Background Citations
1

Figures and Tables from this paper

One Citation

Jointly Learning Consistent Causal Abstractions Over Multiple Interventional Distributions

This paper introduces a first framework for causal abstraction learning between SCMs based on the formalization of abstraction recently proposed by Rischel (2020), and proposes a differentiable programming solution that jointly solves a number of combinatorial sub-problems.

References

SHOWING 1-8 OF 8 REFERENCES

Approximate Causal Abstractions

The account of approximate abstractions for causal models is extended to probabilistic causal models, indicating how and where uncertainty can enter into an approximate abstraction.

Abstracting Causal Models

It is shown that procedures for combining micro-variables into macro-Variables are instances of the notion of strong abstraction, as are all the examples considered by Rubenstein et al. (2017), which takes more seriously all potential interventions in a model, not just the allowed interventions.

Compositional Abstraction Error and a Category of Causal Models

This work develops a framework for model transformations and abstractions with a notion of error that is compositional, and introduces a category of finite interventional causal models and proves that the framework enjoys the desired compositionality properties.

Causal Consistency of Structural Equation Models

This work formalises the notion of consistency in the case of Structural Equation Models (SEMs) by introducing exact transformations between SEMs, which provides a general language to consider the different levels of description in the following three scenarios.

A Unified Framework for Extensive-Form Game Abstraction with Bounds

A unified framework for analyzing abstractions that can express all types of abstractions and solution concepts used in prior papers with performance guarantees---while maintaining comparable bounds on abstraction quality is presented.

Information Theory and Statistical Mechanics

Treatment of the predictive aspect of statistical mechanics as a form of statistical inference is extended to the density-matrix formalism and applied to a discussion of the relation between…

Elements of Information Theory

The author examines the role of entropy, inequality, and randomness in the design of codes and the construction of codes in the rapidly changing environment.

Toward Causal Representation Learning

Fundamental concepts of causal inference are reviewed and related to crucial open problems of machine learning, including transfer and generalization, thereby assaying how causality can contribute to modern machine learning research.