A Measure-Theoretic Axiomatisation of Causality
Authors: Junhyung Park, Simon Buchholz, Bernhard Schölkopf, Krikamol Muandet
NeurIPS 2023 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | Our goal in this paper is to give an axiomatic framework of the forwards direction of Figure 1b, which currently consists of many competing models (see Related Works). As a starting point, we observe that the forwards direction of Figure 1a, i.e. probability theory, has a set of axioms based on measure theory (Axioms 2.1) that are widely accepted and used1, and hence argue that it is natural to take the primitive objects of this framework as the basic building blocks. Despite the fact that all of the existing mathematical frameworks of causality recognise the crucial role that probability plays / should play in any causal theory, it is surprising that few of them try to build directly upon the axioms of probability theory, and those that do fall short in different ways (see Related Works). On the other hand, we place manipulations at the heart of our approach to causality; in other words, we make changes to some parts of a system, and we are interested in what happens to the rest of this system. This manipulative philosophy towards causality is shared by many philosophers [64], and is the essence behind almost all causal frameworks proposed and adopted in the statistics/machine learning community that we are aware of. To this end, we propose the notion of causal spaces (Definition 2.2), constructed by adding causal objects, called causal kernels, directly to probability spaces. We show that causal spaces strictly generalise (the interventional aspects of) existing frameworks, i.e. given any configuration of, for example, a structural causal model or potential outcomes framework, we can construct a causal space that can carry the same (interventional) information. Further, we show that causal spaces can seamlessly support situations where existing frameworks struggle, for example those with hidden confounders, cyclic causal relationships or continuous-time stochastic processes. |
| Researcher Affiliation | Academia | Junhyung Park Empirical Inference Department MPI for Intelligent Systems 72076 Tübingen, Germany junhyung.park@tuebingen.mpg.de Simon Buchholz Empirical Inference Department MPI for Intelligent Systems 72076 Tübingen, Germany simon.buchholz@tuebingen.mpg.de Bernhard Schölkopf Empirical Inference Department MPI for Intelligent Systems 72076 Tübingen, Germany bs@tuebingen.mpg.de Krikamol Muandet CISPA Helmholtz Center for Information Security 66123 Saarbrücken, Germany muandet@cispa.de |
| Pseudocode | No | The paper contains mathematical definitions, axioms, and theorems, but it does not include any pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not contain any statement about releasing open-source code for the described methodology. |
| Open Datasets | No | The paper uses illustrative examples (e.g., 'monthly ice cream sales and shark attacks', 'amount of rice in the market and its price per kg', '1-dimensional Brownian motion') to explain concepts, but these are conceptual examples and not public datasets used for empirical training or evaluation. |
| Dataset Splits | No | The paper is theoretical and does not involve empirical experiments, therefore it does not mention training, validation, or test dataset splits. |
| Hardware Specification | No | The paper is theoretical and does not describe any experimental hardware used. |
| Software Dependencies | No | The paper is theoretical and does not mention any specific software dependencies with version numbers for experimental reproducibility. |
| Experiment Setup | No | The paper is theoretical and does not include details about an experimental setup, such as hyperparameters or system-level training settings. |