Large knowledge graphs increasingly add value to various applications that require machines to recognize and understand queries and their semantics, as in search or question answering systems. Latent variable models have increasingly gained attention for the statistical modeling of knowledge graphs, showing promising results in tasks related to knowledge graph completion and cleaning. Besides storing facts about the world, schema-based knowledge graphs are backed by rich semantic descriptions of entities and relation-types that allow machines to understand the notion of things and their semantic relationships. In this work, we study how type-constraints can generally support the statistical modeling with latent variable models. More precisely, we integrated prior knowledge in form of type-constraints in various state of the art latent variable approaches. Our experimental results show that prior knowledge on relation-types significantly improves these models up to 77 in link-prediction tasks. The achieved improvements are especially prominent when a low model complexity is enforced, a crucial requirement when these models are applied to very large datasets. Unfortunately, type-constraints are neither always available nor always complete e.g., they can become fuzzy when entities lack proper typing. We show that in these cases, it can be beneficial to apply a local closed-world assumption that approximates the semantics of relation-types based on observations made in the data.
Domain and range constraints as given by the KG's schema or via a local closed-world assumption have been exploited very recently in RESCAL @cite_1 @cite_12 , but to the best of our knowledge have not yet been integrated into other latent variable methods nor has their general value been recognized for these models.
@cite_1 @cite_12
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An essential problem in domain adaptation is to understand and make use of distribution changes across domains. For this purpose, we first propose a flexible Generative Domain Adaptation Network (G-DAN) with specific latent variables to capture changes in the generating process of features across domains. By explicitly modeling the changes, one can even generate data in new domains using the generating process with new values for the latent variables in G-DAN. In practice, the process to generate all features together may involve high-dimensional latent variables, requiring dealing with distributions in high dimensions and making it difficult to learn domain changes from few source domains. Interestingly, by further making use of the causal representation of joint distributions, we then decompose the joint distribution into separate modules, each of which involves different low-dimensional latent variables and can be learned separately, leading to a Causal G-DAN (CG-DAN). This improves both statistical and computational efficiency of the learning procedure. Finally, by matching the feature distribution in the target domain, we can recover the target-domain joint distribution and derive the learning machine for the target domain. We demonstrate the efficacy of both G-DAN and CG-DAN in domain generation and cross-domain prediction on both synthetic and real data experiments. The representation of a knowledge graph (KG) in a latent space recently has attracted more and more attention. To this end, some proposed models (e.g., TransE) embed entities and relations of a KG into a "point" vector space by optimizing a global loss function which ensures the scores of positive triplets are higher than negative ones. We notice that these models always regard all entities and relations in a same manner and ignore their (un)certainties. In fact, different entities and relations may contain different certainties, which makes identical certainty insufficient for modeling. Therefore, this paper switches to density-based embedding and propose KG2E for explicitly modeling the certainty of entities and relations, which learn the representations of KGs in the space of multi-dimensional Gaussian distributions. Each entity relation is represented by a Gaussian distribution, where the mean denotes its position and the covariance (currently with diagonal covariance) can properly represent its certainty. In addition, compared with the symmetric measures used in point-based methods, we employ the KL-divergence for scoring triplets, which is a natural asymmetry function for effectively modeling multiple types of relations. We have conducted extensive experiments on link prediction and triplet classification with multiple benchmark datasets (WordNet and Freebase). Our experimental results demonstrate that our method can effectively model the (un)certainties of entities and relations in a KG, and it significantly outperforms state-of-the-art methods (including TransH and TransR). We propose a novel reconstruction-based transfer learning method called latent sparse domain transfer (LSDT) for domain adaptation and visual categorization of heterogeneous data. For handling cross-domain distribution mismatch, we advocate reconstructing the target domain data with the combined source and target domain data points based on @math -norm sparse coding. Furthermore, we propose a joint learning model for simultaneous optimization of the sparse coding and the optimal subspace representation. In addition, we generalize the proposed LSDT model into a kernel-based linear nonlinear basis transformation learning framework for tackling nonlinear subspace shifts in reproduced kernel Hilbert space. The proposed methods have three advantages: 1) the latent space and the reconstruction are jointly learned for pursuit of an optimal subspace transfer; 2) with the theory of sparse subspace clustering, a few valuable source and target data points are formulated to reconstruct the target data with noise (outliers) from source domain removed during domain adaptation, such that the robustness is guaranteed; and 3) a nonlinear projection of some latent space with kernel is easily generalized for dealing with highly nonlinear domain shift (e.g., face poses). Extensive experiments on several benchmark vision data sets demonstrate that the proposed approaches outperform other state-of-the-art representation-based domain adaptation methods. In domain adaptation, maximum mean discrepancy (MMD) has been widely adopted as a discrepancy metric between the distributions of source and target domains. However, existing MMD-based domain adaptation methods generally ignore the changes of class prior distributions, i.e., class weight bias across domains. This remains an open problem but ubiquitous for domain adaptation, which can be caused by changes in sample selection criteria and application scenarios. We show that MMD cannot account for class weight bias and results in degraded domain adaptation performance. To address this issue, a weighted MMD model is proposed in this paper. Specifically, we introduce class-specific auxiliary weights into the original MMD for exploiting the class prior probability on source and target domains, whose challenge lies in the fact that the class label in target domain is unavailable. To account for it, our proposed weighted MMD model is defined by introducing an auxiliary weight for each class in the source domain, and a classification EM algorithm is suggested by alternating between assigning the pseudo-labels, estimating auxiliary weights and updating model parameters. Extensive experiments demonstrate the superiority of our weighted MMD over conventional MMD for domain adaptation.