We propose an approach to symbolic regression based on a novel variational autoencoder for generating hierarchical structures, HVAE. It combines simple atomic units with shared weights to recursively encode and decode the individual nodes in the hierarchy. Encoding is performed bottom-up and decoding top-down. We empirically show that HVAE can be trained efficiently with small corpora of mathematical expressions and can accurately encode expressions into a smooth low-dimensional latent space. The latter can be efficiently explored with various optimization methods to address the task of symbolic regression. Indeed, random search through the latent space of HVAE performs better than random search through expressions generated by manually crafted probabilistic grammars for mathematical expressions. Finally, EDHiE system for symbolic regression, which applies an evolutionary algorithm to the latent space of HVAE, reconstructs equations from a standard symbolic regression benchmark better than a state-of-the-art system based on a similar combination of deep learning and evolutionary algorithms.

Increasing quantities of semantic resources offer a wealth of human knowledge, but their growth also increases the probability of wrong knowledge base entries. The development of approaches that identify potentially spurious parts of a given knowledge base is therefore highly relevant. We propose an approach for ontology completion that transforms an ontology into a graph and recommends missing edges using structure-only link analysis methods. By systematically evaluating thirteen methods (some for knowledge graphs) on eight different semantic resources, including Gene Ontology, Food Ontology, Marine Ontology, and similar ontologies, we demonstrate that a structure-only link analysis can offer a scalable and computationally efficient ontology completion approach for a subset of analyzed data sets. To the best of our knowledge, this is currently the most extensive systematic study of the applicability of different types of link analysis methods across semantic resources from different domains. It demonstrates that by considering symbolic node embeddings, explanations of the predictions (links) can be obtained, making this branch of methods potentially more valuable than black-box methods.

Learning from complex real-life networks is a lively research area, with recent advances in learning information-rich, low-dimensional network node representations. However, state-of-the-art methods are not necessarily interpretable and are therefore not fully applicable to sensitive settings in biomedical or user profiling tasks, where explicit bias detection is highly relevant. The proposed SNoRe (Symbolic Node Representations) algorithm is capable of learning symbolic, human-understandable representations of individual network nodes, based on the similarity of neighborhood hashes which serve as features. SNoRe’s interpretable features are suitable for direct explanation of individual predictions, which we demonstrate by coupling it with the widely used instance explanation tool SHAP to obtain nomograms representing the relevance of individual features for a given classification. To our knowledge, this is one of the first such attempts in a structural node embedding setting. In the experimental evaluation on eleven real-life datasets, SNoRe proved to be competitive to strong baselines, such as variational graph autoencoders, node2vec and LINE. The vectorized implementation of SNoRe scales to large networks, making it suitable for contemporary network learning and analysis tasks.

We propose an approach to symbolic regression based on a novel variational autoencoder for generating hierarchical structures, HVAE. It combines simple atomic units with shared weights to recursively encode and decode the individual nodes in the hierarchy. Encoding is performed bottom-up and decoding top-down. We empirically show that HVAE can be trained efficiently with small corpora of mathematical expressions and can accurately encode expressions into a smooth low-dimensional latent space. The latter can be efficiently explored with various optimization methods to address the task of symbolic regression. Indeed, random search through the latent space of HVAE performs better than random search through expressions generated by manually crafted probabilistic grammars for mathematical expressions. Finally, EDHiE system for symbolic regression, which applies an evolutionary algorithm to the latent space of HVAE, reconstructs equations from a standard symbolic regression benchmark better than a state-of-the-art system based on a similar combination of deep learning and evolutionary algorithms.ž