Compression versus Accuracy: A Hierarchy of Lifted Models
This work addresses a specific bottleneck in probabilistic inference for researchers, offering incremental improvements in interpretability and efficiency.
The paper tackles the problem of selecting hyperparameters for approximate lifted inference in probabilistic graphical models, presenting a hyperparameter-free hierarchical approach that efficiently computes a hierarchy of models with error bounds, enabling explicit trade-offs between compression and accuracy.
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.