arXiv subjects

Maximilian Nickel

Publications and source records attributed to Maximilian Nickel.

42 records · Page 3Linked to original sources

arXiv2017

Complex and Holographic Embeddings of Knowledge Graphs: A Comparison

Embeddings of knowledge graphs have received significant attention due to their excellent performance for tasks like link prediction and entity resolution. In this short paper, we are providing a comparison of two state-of-the-art knowledge graph embeddings for which their equivalence has recently been established, i.e., ComplEx and HolE [Nickel, Rosasco, and Poggio, 2016; Trouillon et al., 2016; Hayashi and Shimbo, 2017]. First, we briefly review both models and discuss how their scoring functions are equivalent. We then analyze the discrepancy of results reported in the original articles, and show experimentally that they are likely due to the use of different loss functions. In further experiments, we evaluate the ability of both models to embed symmetric and antisymmetric patterns. Finally, we discuss advantages and disadvantages of both models and under which conditions one would be preferable to the other.

cs.LG↗

arXiv2017

Poincaré Embeddings for Learning Hierarchical Representations

Representation learning has become an invaluable approach for learning from symbolic data such as text and graphs. However, while complex symbolic datasets often exhibit a latent hierarchical structure, state-of-the-art methods typically learn embeddings in Euclidean vector spaces, which do not account for this property. For this purpose, we introduce a new approach for learning hierarchical representations of symbolic data by embedding them into hyperbolic space -- or more precisely into an n-dimensional Poincaré ball. Due to the underlying hyperbolic geometry, this allows us to learn parsimonious representations of symbolic data by simultaneously capturing hierarchy and similarity. We introduce an efficient algorithm to learn the embeddings based on Riemannian optimization and show experimentally that Poincaré embeddings outperform Euclidean embeddings significantly on data with latent hierarchies, both in terms of representation capacity and in terms of generalization ability.

cs.AI↗

arXiv2016

Relational Models

We provide a survey on relational models. Relational models describe complete networked {domains by taking into account global dependencies in the data}. Relational models can lead to more accurate predictions if compared to non-relational machine learning approaches. Relational models typically are based on probabilistic graphical models, e.g., Bayesian networks, Markov networks, or latent variable models. Relational models have applications in social networks analysis, the modeling of knowledge graphs, bioinformatics, recommendation systems, natural language processing, medical decision support, and linked data.

cs.AI↗

arXiv2015

Holographic Embeddings of Knowledge Graphs

Learning embeddings of entities and relations is an efficient and versatile method to perform machine learning on relational data such as knowledge graphs. In this work, we propose holographic embeddings (HolE) to learn compositional vector space representations of entire knowledge graphs. The proposed method is related to holographic models of associative memory in that it employs circular correlation to create compositional representations. By using correlation as the compositional operator HolE can capture rich interactions but simultaneously remains efficient to compute, easy to train, and scalable to very large datasets. In extensive experiments we show that holographic embeddings are able to outperform state-of-the-art methods for link prediction in knowledge graphs and relational learning benchmark datasets.

cs.AI↗

arXiv2015

A Review of Relational Machine Learning for Knowledge Graphs

Relational machine learning studies methods for the statistical analysis of relational, or graph-structured, data. In this paper, we provide a review of how such statistical models can be "trained" on large knowledge graphs, and then used to predict new facts about the world (which is equivalent to predicting new edges in the graph). In particular, we discuss two fundamentally different kinds of statistical relational models, both of which can scale to massive datasets. The first is based on latent feature models such as tensor factorization and multiway neural networks. The second is based on mining observable patterns in the graph. We also show how to combine these latent and observable models to get improved modeling power at decreased computational cost. Finally, we discuss how such statistical models of graphs can be combined with text-based information extraction methods for automatically constructing knowledge graphs from the Web. To this end, we also discuss Google's Knowledge Vault project as an example of such combination.

stat.ML↗

arXiv2013

Logistic Tensor Factorization for Multi-Relational Data

Tensor factorizations have become increasingly popular approaches for various learning tasks on structured data. In this work, we extend the RESCAL tensor factorization, which has shown state-of-the-art results for multi-relational learning, to account for the binary nature of adjacency tensors. We study the improvements that can be gained via this approach on various benchmark datasets and show that the logistic extension can improve the prediction results significantly.

stat.ML↗