Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in [1].
The d-Separation Criterion in Categorical Probability
Authors: Tobias Fritz, Andreas Klingler
JMLR 2023 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | In this work, we study this problem in the context of categorical probability theory by introducing a categorical definition of causal models, a categorical notion of d-separation, and proving an abstract version of the d-separation criterion. This approach has two main benefits. First, categorical d-separation is a very intuitive criterion based on topological connectedness. Second, our results apply both to measure-theoretic probability (with standard Borel spaces) and beyond probability theory, including to deterministic and possibilistic networks. It therefore provides a clean proof of the equivalence of local and global Markov properties with causal compatibility for continuous and mixed random variables as well as deterministic and possibilistic variables. |
| Researcher Affiliation | Academia | Tobias Fritz EMAIL Department of Mathematics University of Innsbruck 6020 Innsbruck, Austria Andreas Klingler EMAIL Institute for Theoretical Physics University of Innsbruck 6020 Innsbruck, Austria |
| Pseudocode | No | The paper uses string diagrams to illustrate concepts and categorical operations, such as 'del X = copy X =', but these are visual representations of mathematical structures and not structured pseudocode or algorithm blocks describing a procedure. |
| Open Source Code | No | The paper does not contain any explicit statement about releasing source code for the methodology described. It provides license information for the paper itself and its attribution requirements, but no mention of code. |
| Open Datasets | No | The paper is theoretical and focuses on mathematical definitions and proofs within categorical probability theory. It does not perform empirical studies or use specific datasets, thus no information on publicly available or open datasets is provided. |
| Dataset Splits | No | This paper is theoretical in nature and does not involve experimental evaluation using datasets. Therefore, there is no mention of dataset splits (e.g., training, testing, validation splits). |
| Hardware Specification | No | The paper is a theoretical work in categorical probability theory and does not describe any experiments or computational tasks that would require specific hardware specifications. |
| Software Dependencies | No | The paper is entirely theoretical, presenting mathematical definitions and proofs. It does not describe any software implementations or list specific software dependencies with version numbers for experimental reproducibility. |
| Experiment Setup | No | The paper is theoretical, providing an abstract framework and proofs related to the d-separation criterion in categorical probability. It does not include any experimental results, and therefore, no experimental setup details such as hyperparameters or training settings are provided. |