The effectiveness of knowledge graph embedding (KGE) largely depends on the
ability to model intrinsic relation patterns and mapping properties. However,
existing approaches can only capture some of them with insufficient modeling
capacity. In this work, we propose a more powerful KGE framework named HousE,
which involves a novel parameterization based on two kinds of Householder
transformations: (1) Householder rotations to achieve superior capacity of
modeling relation patterns; (2) Householder projections to handle sophisticated
relation mapping properties. Theoretically, HousE is capable of modeling
crucial relation patterns and mapping properties simultaneously. Besides, HousE
is a generalization of existing rotation-based models while extending the
rotations to high-dimensional spaces. Empirically, HousE achieves new
state-of-the-art performance on five benchmark datasets. Our code is available
at this https URL.

本文提出了一种强大的知识图谱嵌入 (knowledge graph embedding) 框架 HousE，利用两种 Householder 变换进行参数化，从而实现了对于关系模式和映射属性的建模能力，并在五个基准数据集上取得了新的最佳表现。

HousE: 带豪斯霍尔德参数化的知识图谱嵌入

HousE: Knowledge Graph Embedding with Householder Parameterization

We consider probabilistic PCA and related factor models from a Bayesian
perspective. These models are in general not identifiable as the likelihood has
a rotational symmetry. This gives rise to complicated posterior distributions
with continuous subspaces of equal density and thus hinders efficiency of
inference as well as interpretation of obtained parameters. In particular,
posterior averages over factor loadings become meaningless and only model
predictions are unambiguous. Here, we propose a parameterization based on
Householder transformations, which remove the rotational symmetry of the
posterior. Furthermore, by relying on results from random matrix theory, we
establish the parameter distribution which leaves the model unchanged compared
to the original rotationally symmetric formulation. In particular, we avoid the
need to compute the Jacobian determinant of the parameter transformation. This
allows us to efficiently implement probabilistic PCA in a rotation invariant
fashion in any state of the art toolbox. Here, we implemented our model in the
probabilistic programming language Stan and illustrate it on several examples.

文章从贝叶斯角度考虑了概率主成分分析和相关因子模型。提出了一种基于 Householder 变换的参数化方法，解决了模型识别性问题，并使用随机矩阵理论得到了使模型不变的参数分布，从而避免了计算参数转换的 Jacobian 行列式的需要。在 Stan 等工具中以旋转不变的方式高效实现了算法，并在多个实例上进行了验证。

贝叶斯主成分分析的旋转不变 Householder 参数化

Rotation Invariant Householder Parameterization for Bayesian PCA

Variational auto-encoders (VAE) are scalable and powerful generative models.
However, the choice of the variational posterior determines tractability and
flexibility of the VAE. Commonly, latent variables are modeled using the normal
distribution with a diagonal covariance matrix. This results in computational
efficiency but typically it is not flexible enough to match the true posterior
distribution. One fashion of enriching the variational posterior distribution
is application of normalizing flows, i.e., a series of invertible
transformations to latent variables with a simple posterior. In this paper, we
follow this line of thinking and propose a volume-preserving flow that uses a
series of Householder transformations. We show empirically on MNIST dataset and
histopathology data that the proposed flow allows to obtain more flexible
variational posterior and competitive results comparing to other normalizing
flows.

本论文提出了一种基于 Householder 变换的体积保存流方法，改进了变分后验分布的灵活性并在 MNIST 数据集和组织病理学数据中获得了理想的结果。