Relational Marginal Problems: Theory and Estimation
Authors: Ondřej Kuželka, Yuyi Wang, Jesse Davis, Steven Schockaert
AAAI 2018 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | First, we compare two different notions of relational marginals. Second, we show a duality between the resulting relational marginal problems and the maximum likelihood estimation of the parameters of relational models, which generalizes a well-known duality from the propositional setting. Third, by exploiting the relational marginal formulation, we present a statistically sound method to learn the parameters of relational models that will be applied in settings where the number of constants differs between the training and test data. Furthermore, based on a relational generalization of marginal polytopes, we characterize cases where the standard estimators based on feature s number of true groundings needs to be adjusted and we quantitatively characterize the consequences of these adjustments. Fourth, we prove bounds on expected errors of the estimated parameters, which allows us to lower-bound, among other things, the effective sample size of relational training data. |
| Researcher Affiliation | Academia | Ondˇrej Kuˇzelka Cardiff University, UK Kuzelka O@cardiff.ac.uk Yuyi Wang ETH Zurich, Switzerland yuwang@ethz.ch Jesse Davis KU Leuven, Belgium jesse.davis@cs.kuleuven.be Steven Schockaert Cardiff University, UK Schockaert S1@cardiff.ac.uk |
| Pseudocode | No | The paper does not contain structured pseudocode or algorithm blocks. |
| Open Source Code | No | The paper links to an online appendix (https://arxiv.org/abs/1709.05825) but does not contain an explicit statement about providing source code or a direct link to a code repository for the methodology described. |
| Open Datasets | No | The paper discusses 'training data' conceptually and uses 'Facebook' as an example, but it does not specify any named public dataset or provide access information (link, DOI, citation) for a dataset used in its theoretical analysis. |
| Dataset Splits | No | The paper is theoretical and does not conduct empirical experiments, therefore it does not provide specific dataset split information for training, validation, or testing. |
| Hardware Specification | No | The paper is theoretical and does not conduct empirical experiments, therefore it does not provide specific hardware details used for running experiments. |
| Software Dependencies | No | The paper is theoretical and does not describe an implementation that would require specific software dependencies with version numbers. |
| Experiment Setup | No | The paper is theoretical and does not conduct empirical experiments, therefore it does not provide specific experimental setup details such as hyperparameters or training configurations. |