A variety of lifted inference algorithms, which exploit model symmetry to
reduce computational cost, have been proposed to render inference tractable in
probabilistic relational models. Most existing lifted inference algorithms
operate only over discrete domains or continuous domains with restricted
potential functions, e.g., Gaussian. We investigate two approximate lifted
variational approaches that are applicable to hybrid domains and expressive
enough to capture multi-modality. We demonstrate that the proposed variational
methods are both scalable and can take advantage of approximate model
symmetries, even in the presence of a large amount of continuous evidence. We
demonstrate that our approach compares favorably against existing
message-passing based approaches in a variety of settings. Finally, we present
a sufficient condition for the Bethe approximation to yield a non-trivial
estimate over the marginal polytope.

本文研究了适用于混合域的近似变分方法及其对称性，展示了这些方法较现有的基于信息传递的方法更具有可伸缩性和优越性能，并提出了 Bethe 近似在建模多样本方面的一个充分条件。

抬升的混合变分推断

Lifted Hybrid Variational Inference

In many supervised learning tasks, the entities to be labeled are related to
each other in complex ways and their labels are not independent. For example,
in hypertext classification, the labels of linked pages are highly correlated.
A standard approach is to classify each entity independently, ignoring the
correlations between them. Recently, Probabilistic Relational Models, a
relational version of Bayesian networks, were used to define a joint
probabilistic model for a collection of related entities. In this paper, we
present an alternative framework that builds on (conditional) Markov networks
and addresses two limitations of the previous approach. First, undirected
models do not impose the acyclicity constraint that hinders representation of
many important relational dependencies in directed models. Second, undirected
models are well suited for discriminative training, where we optimize the
conditional likelihood of the labels given the features, which generally
improves classification accuracy. We show how to train these models
effectively, and how to use approximate probabilistic inference over the
learned model for collective classification of multiple related entities. We
provide experimental results on a webpage classification task, showing that
accuracy can be significantly improved by modeling relational dependencies.

本文提出一种基于 (条件) 马尔科夫网络的框架，可以 effectively 地训练 probabilistic relational models，并使用近似概率推断对多个相关对象进行 collective classification，从而解决了先前方法的两个限制：有向模型无法表示许多重要的关系依赖性和难以用于判别式训练。在网页分类任务上的实验证明，建模关系依赖性可以显著提高分类准确性。