The Inflation Technique for Causal Inference with Latent Variables
| Autor: | Elie Wolfe, Tobias Fritz, Robert W. Spekkens |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
FOS: Computer and information sciences
Statistics and Probability Inflation media_common.quotation_subject FOS: Physical sciences Machine Learning (stat.ML) Mathematics - Statistics Theory Statistics Theory (math.ST) Latent variable Causal structure causal compatibility inequalities 01 natural sciences QA273-280 010305 fluids & plasmas hardy paradox Methodology (stat.ME) bell inequalities Statistics - Machine Learning 0103 physical sciences QA1-939 FOS: Mathematics 010306 general physics Statistics - Methodology Mathematics media_common Causal model Quantum Physics gpt causal models triangle scenario Probability and statistics inflation technique causal inference with latent variables quantum causal models Causal inference marginal problem Probability distribution Statistics Probability and Uncertainty Marginal distribution Quantum Physics (quant-ph) graph symmetries Probabilities. Mathematical statistics Mathematical economics |
| Zdroj: | Journal of Causal Inference, Vol 7, Iss 2, Pp 156-65 (2019) |
| ISSN: | 2193-3685 2193-3677 |
| DOI: | 10.1515/jci-2017-0020 |
| Popis: | The problem of causal inference is to determine if a given probability distribution on observed variables is compatible with some causal structure. The difficult case is when the causal structure includes latent variables. We here introduce the $\textit{inflation technique}$ for tackling this problem. An inflation of a causal structure is a new causal structure that can contain multiple copies of each of the original variables, but where the ancestry of each copy mirrors that of the original. To every distribution of the observed variables that is compatible with the original causal structure, we assign a family of marginal distributions on certain subsets of the copies that are compatible with the inflated causal structure. It follows that compatibility constraints for the inflation can be translated into compatibility constraints for the original causal structure. Even if the constraints at the level of inflation are weak, such as observable statistical independences implied by disjoint causal ancestry, the translated constraints can be strong. We apply this method to derive new inequalities whose violation by a distribution witnesses that distribution's incompatibility with the causal structure (of which Bell inequalities and Pearl's instrumental inequality are prominent examples). We describe an algorithm for deriving all such inequalities for the original causal structure that follow from ancestral independences in the inflation. For three observed binary variables with pairwise common causes, it yields inequalities that are stronger in at least some aspects than those obtainable by existing methods. We also describe an algorithm that derives a weaker set of inequalities but is more efficient. Finally, we discuss which inflations are such that the inequalities one obtains from them remain valid even for quantum (and post-quantum) generalizations of the notion of a causal model. Minor final corrections, updated to match the published version as closely as possible |
| Databáze: | OpenAIRE |
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