Faithfulness of Probability Distributions and Graphs
Authors: Kayvan Sadeghi
JMLR 2017 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | A main question in graphical models and causal inference is whether, given a probability distribution P (which is usually an underlying distribution of data), there is a graph (or graphs) to which P is faithful. The main goal of this paper is to provide a theoretical answer to this problem. We work with general independence models, which contain probabilistic independence models as a special case. We exploit a generalization of ordering, called preordering, of the nodes of (mixed) graphs. This allows us to provide sufficient conditions for a given independence model to be Markov to a graph with the minimum possible number of edges, and more importantly, necessary and sufficient conditions for a given probability distribution to be faithful to a graph. |
| Researcher Affiliation | Academia | Kayvan Sadeghi EMAIL Statistical Laboratory University of Cambridge Centre for Mathematical Sciences, Wilberforce Road Cambridge, CB3 0WB, United Kingdom |
| Pseudocode | No | The paper presents theoretical concepts, definitions, propositions, theorems, and proofs. It does not include any explicitly labeled pseudocode blocks or algorithms with structured, code-like formatting. |
| Open Source Code | No | The paper mentions future work on an algorithm: "We plan on providing the details of this algorithm elsewhere." This indicates a future release, not current public availability of source code for the methodology described in this paper. |
| Open Datasets | No | The paper is theoretical and focuses on mathematical conditions for faithfulness of probability distributions and graphs. It does not describe any experiments performed on specific datasets or provide access information for any datasets. |
| Dataset Splits | No | The paper is theoretical and does not involve empirical experiments with data. Therefore, there is no mention of dataset splits for training, validation, or testing. |
| Hardware Specification | No | The paper is purely theoretical, presenting mathematical proofs and conditions. It does not describe any computational experiments or specify any hardware used. |
| Software Dependencies | No | The paper is theoretical and does not involve any implementation or computational experiments. Consequently, it does not list any specific software dependencies with version numbers. |
| Experiment Setup | No | The paper is theoretical and focuses on mathematical conditions and proofs. It does not describe any experimental setup, hyperparameters, training configurations, or any other details related to conducting experiments. |