A Measure-Theoretic Axiomatisation of Causality
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866916276212858880 |
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| author | Park, Junhyung Buchholz, Simon Schölkopf, Bernhard Muandet, Krikamol |
| author_facet | Park, Junhyung Buchholz, Simon Schölkopf, Bernhard Muandet, Krikamol |
| contents | Causality is a central concept in a wide range of research areas, yet there is still no universally agreed axiomatisation of causality. We view causality both as an extension of probability theory and as a study of \textit{what happens when one intervenes on a system}, and argue in favour of taking Kolmogorov's measure-theoretic axiomatisation of probability as the starting point towards an axiomatisation of causality. To that end, we propose the notion of a \textit{causal space}, consisting of a probability space along with a collection of transition probability kernels, called \textit{causal kernels}, that encode the causal information of the space. Our proposed framework is not only rigorously grounded in measure theory, but it also sheds light on long-standing limitations of existing frameworks including, for example, cycles, latent variables and stochastic processes. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2305_17139 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A Measure-Theoretic Axiomatisation of Causality Park, Junhyung Buchholz, Simon Schölkopf, Bernhard Muandet, Krikamol Artificial Intelligence Statistics Theory Causality is a central concept in a wide range of research areas, yet there is still no universally agreed axiomatisation of causality. We view causality both as an extension of probability theory and as a study of \textit{what happens when one intervenes on a system}, and argue in favour of taking Kolmogorov's measure-theoretic axiomatisation of probability as the starting point towards an axiomatisation of causality. To that end, we propose the notion of a \textit{causal space}, consisting of a probability space along with a collection of transition probability kernels, called \textit{causal kernels}, that encode the causal information of the space. Our proposed framework is not only rigorously grounded in measure theory, but it also sheds light on long-standing limitations of existing frameworks including, for example, cycles, latent variables and stochastic processes. |
| title | A Measure-Theoretic Axiomatisation of Causality |
| topic | Artificial Intelligence Statistics Theory |
| url | https://arxiv.org/abs/2305.17139 |