Lifting probabilistic graphical models and developing lifted inference algorithms aim to use higher level groups of random variables instead of individual instances. In the past, many inference algorithms for discrete probabilistic graphical models have been lifted. Lifting continuous probabilistic graphical models has played a minor role. Since many real-world applications involve continuous random variables, this article turns its focus to lifting approaches for Gaussian Bayesian networks. Specifically, we present algorithms for constructing a lifted joint distribution for scenarios of sequences of overlapping and non-overlapping logical variables. We present operations that work in a fully lifted way including addition, multiplication, and inversion. We present how the operations can be used for lifted query answering algorithms and extend the existing query answering algorithm by a new way of evidence handling. The new way of evidence handling groups evidence that has the same effect on its neighboring variables in cases of partial overlap between the logical-variable sequences. In the theoretical complexity analysis and the experimental evaluation, we show under which conditions the existing lifted approach and the new lifted approach including evidence grouping lead to the most time savings compared to the grounded approach.

中文翻译：

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提升高斯贝叶斯网络的扩展观点

提升概率图形模型和开发提升推理算法的目的是使用更高级别的随机变量组而不是单个实例。过去，许多离散概率图模型的推理算法已经被解除。提升连续概率图模型发挥了次要作用。由于许多现实世界的应用涉及连续随机变量，因此本文将重点转向高斯贝叶斯网络的提升方法。具体来说，我们提出了针对重叠和非重叠逻辑变量序列场景构建提升联合分布的算法。我们展示以完全提升的方式工作的运算，包括加法、乘法和求逆。我们介绍了如何将这些操作用于提升的查询应答算法，并通过新的证据处理方式扩展现有的查询应答算法。在逻辑变量序列之间部分重叠的情况下，证据处理的新方法对对其相邻变量具有相同影响的证据进行分组。在理论复杂性分析和实验评估中，我们展示了在哪些条件下，现有的提升方法和新的提升方法（包括证据分组）与扎根方法相比可以节省最多时间。