Multi-Relational Learning at Scale with ADMM

The complex graph structure of the Web - with different relations or edge types - has motivated a large body of research tackling the challenge of mining multi-relational data in the presence of noise, partial inconsistencies, ambiguities, or duplicate entities. State-of-the-art advances in this field are relevant to many applications such as link prediction [1], Resource Description Framework (RDF) mining [2], entity linking [3], recommender systems [4], and natural language processing [5]. However, new paradigms are still needed for statistical and computational inference for very large multi-relational datasets, like the ones produced at massive scale in projects such as the Google's Knowledge Graph [6], YAGO [7], and in Semantic Web initiatives such as DBpedia [8]. Factorization models are considered state-of-the-art approaches for Statistical Relational Learning (SRL) in which they have exhibited a high predictive performance [9], [10], [11]. Factorization models for multi-relational data associate entities and relations with latent feature vectors and model predictions about unknown relationships through operations on these vectors (e.g., dot products). Optimizing the predictions for a number of relations can be seen as a prediction task with multiple target variables. For example, multi-target models can support information retrieval tasks in Linked Open Data bases like DBPedia by providing estimates of facts, that are neither explicitly stated in the knowledge base nor can be inferred from logical entailment, enabling probabilistic queries on such databases [1], [2]. Another example in the context of social web recommender systems, is that such services are not only interested in recommending, for instance, news items to a user but also recommending other users as potential new friends. State-of-the-art factorization models approach the multitarget prediction task by sharing the parameters used for all target relations.