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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.22288 |
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| _version_ | 1866914012442132480 |
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| author | Speller, Jan Luttermann, Malte Gehrke, Marcel Braun, Tanya |
| author_facet | Speller, Jan Luttermann, Malte Gehrke, Marcel Braun, Tanya |
| contents | Probabilistic graphical models that encode indistinguishable objects and relations among them use first-order logic constructs to compress a propositional factorised model for more efficient (lifted) inference. To obtain a lifted representation, the state-of-the-art algorithm Advanced Colour Passing (ACP) groups factors that represent matching distributions. In an approximate version using $\varepsilon$ as a hyperparameter, factors are grouped that differ by a factor of at most $(1\pm \varepsilon)$. However, finding a suitable $\varepsilon$ is not obvious and may need a lot of exploration, possibly requiring many ACP runs with different $\varepsilon$ values. Additionally, varying $\varepsilon$ can yield wildly different models, leading to decreased interpretability. Therefore, this paper presents a hierarchical approach to lifted model construction that is hyperparameter-free. It efficiently computes a hierarchy of $\varepsilon$ values that ensures a hierarchy of models, meaning that once factors are grouped together given some $\varepsilon$, these factors will be grouped together for larger $\varepsilon$ as well. The hierarchy of $\varepsilon$ values also leads to a hierarchy of error bounds. This allows for explicitly weighing compression versus accuracy when choosing specific $\varepsilon$ values to run ACP with and enables interpretability between the different models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_22288 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Compression versus Accuracy: A Hierarchy of Lifted Models Speller, Jan Luttermann, Malte Gehrke, Marcel Braun, Tanya Artificial Intelligence Probabilistic graphical models that encode indistinguishable objects and relations among them use first-order logic constructs to compress a propositional factorised model for more efficient (lifted) inference. To obtain a lifted representation, the state-of-the-art algorithm Advanced Colour Passing (ACP) groups factors that represent matching distributions. In an approximate version using $\varepsilon$ as a hyperparameter, factors are grouped that differ by a factor of at most $(1\pm \varepsilon)$. However, finding a suitable $\varepsilon$ is not obvious and may need a lot of exploration, possibly requiring many ACP runs with different $\varepsilon$ values. Additionally, varying $\varepsilon$ can yield wildly different models, leading to decreased interpretability. Therefore, this paper presents a hierarchical approach to lifted model construction that is hyperparameter-free. It efficiently computes a hierarchy of $\varepsilon$ values that ensures a hierarchy of models, meaning that once factors are grouped together given some $\varepsilon$, these factors will be grouped together for larger $\varepsilon$ as well. The hierarchy of $\varepsilon$ values also leads to a hierarchy of error bounds. This allows for explicitly weighing compression versus accuracy when choosing specific $\varepsilon$ values to run ACP with and enables interpretability between the different models. |
| title | Compression versus Accuracy: A Hierarchy of Lifted Models |
| topic | Artificial Intelligence |
| url | https://arxiv.org/abs/2505.22288 |