Dangling entities are common in knowledge graphs but there is a lack of research on entity alignment involving them. Most existing studies leverage neural network methods through supervised learning. However, these data-driven methods suffer from poor interpretability and high computation overhead. In this paper, we propose a Simple Unsupervised Dangling entity detection and entity Alignment method (SUDA) 1 without employing neural networks. Our method consists of three modules: entity embedding, dangling entity detection, and entity alignment. While the state-of-the-art Simple but Effective Unsupervised entity alignment method (SEU) 2 is incapable of dealing with dangling entities, SUDA further extends it and addresses the bilateral dangling entities problem. Theoretical proof of our method is given. We also design a new adjacent matrix for incorporating richer entity relations. Then we construct entity similarity outlier intervals to detect dangling entities and align entities through assignment problem after removing them. Extensive experiments demonstrate that our method outperforms those supervised and unsupervised methods . Additionally, in the entity alignment tasks, SUDA consumes less runtime compared to neural network methods, while maintaining high efficiency, interpretability, and stability. Code is available at https://github.com/skyccong/SUDA.git .

Point processes provide a powerful framework for modeling the distribution and interactions of events in time or space. Their flexibility has given rise to a variety of sophisticated models in statistics and machine learning, yet model diagnostic and criticism techniques remain underdeveloped. In this work, we propose a general Stein operator for point processes based on the Papangelou conditional intensity function. We then establish a kernel goodness-of-fit test by defining a Stein discrepancy measure for general point processes. Notably, our test also applies to non-Poisson point processes whose intensity functions contain intractable normalization constants due to the presence of complex interactions among points. We apply our proposed test to several point process models, and show that it outperforms a two-sample test based on the maximum mean discrepancy.

In many complex domains, the input data are often not suited for the typical vector representations used in deep learning models. For example, in relational learning and computer vision tasks, the data are often better represented as sets (e.g., the neighborhood of a node, a cloud of points). In these cases, a key challenge is to learn an embedding function that is invariant to permutations of the input. While there has been some recent work on principled methods for learning permutation-invariant representations of sets, these approaches are limited in their applicability to set-of-sets (SoS) tasks, such as subgraph prediction and scene classification. In this work, we develop a deep neural network framework to learn inductive SoS embeddings that are invariant to SoS permutations. Specifically, we propose HATS, a hierarchical sequence model with attention mechanisms for inductive set-of-sets embeddings. We develop stochastic optimization and inference methods for learning HATS, and our experiments demonstrate that HATS achieves superior performance across a wide range of set-of-sets tasks.

Ridge regression is a variant of regularized least squares regression that is particularly suitable in settings where the number of predictor variables greatly exceeds the number of observations. We present a simple, iterative, sketching-based algorithm for ridge regression that guarantees high-quality approximations to the optimal solution vector. Our analysis builds upon two simple structural results that boil down to randomized matrix multiplication, a fundamental and well-understood primitive of randomized linear algebra. An important contribution of our work is the analysis of the behavior of subsampled ridge regression problems when the ridge leverage scores are used: we prove that accurate approximations can be achieved by a sample whose size depends on the degrees of freedom of the ridge-regression problem rather than the dimensions of the design matrix. Our experimental evaluations verify our theoretical results on both real and synthetic data.

Recent work has combined Stein’s method with reproducing kernel Hilbert space theory to develop nonparametric goodness-of-fit tests for un-normalized probability distributions. However, the currently available tests apply exclusively to distributions with smooth density functions. In this work, we introduce a kernelized Stein discrepancy measure for discrete spaces, and develop a nonparametric goodness-of-fit test for discrete distributions with intractable normalization constants. Furthermore, we propose a general characterization of Stein operators that encompasses both discrete and continuous distributions, providing a recipe for constructing new Stein operators. We apply the proposed goodness-of-fit test to three statistical models involving discrete distributions, and our experiments show that the proposed test typically outperforms a two-sample test based on the maximum mean discrepancy.