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We present an Expectation-Maximization algorithm for the fractal inverse problem: the problem of fitting a fractal model to data. In our setting the fractals are Iterated Function Systems (IFS), with similitudes as the family of transformations. The data is a point cloud in ${\mathbb R}^H$ with arbitrary dimension $H$. Each IFS defines a probability distribution on ${\mathbb R}^H$, so that the fractal inverse problem can be cast as a problem of parameter estimation. We show that the algorithm reconstructs well-known fractals from data, with the model converging to high precision parameters. We also show the utility of the model as an approximation for datasources outside the IFS model class.

Knowledge bases play a crucial role in many applications, for example question answering and information retrieval. Despite the great effort invested in creating and maintaining them, even the largest representatives (e.g., Yago, DBPedia or Wikidata) are highly incomplete. We introduce relational graph convolutional networks (R-GCNs) and apply them to two standard knowledge base completion tasks: link prediction (recovery of missing facts, i.e.~subject-predicate-object triples) and entity classification (recovery of missing attributes of entities). R-GCNs are a generalization of graph convolutional networks, a recent class of neural networks operating on graphs, and are developed specifically to deal with highly multi-relational data, characteristic of realistic knowledge bases. Our methods achieve competitive performance on standard benchmarks for both tasks, demonstrating especially promising results on the challenging FB15k-237 subset of Freebase.