Sebastian Mežnar

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.

Understanding how information propagates in real-life complex networks yields a better understanding of dynamical processes such as misinformation or epidemic spreading. With the recent resurgence of graph neural networks as a powerful predictive methodology, many network properties can be studied in terms of their predictability and as such offer a novel view on the studied process, with the direct application of fast predictions that are complementary to resource-intensive simulations. We investigated whether graph neural networks can be used to predict the effect of an epidemic, should it start from a given individual (patient zero). We reformulate this problem as node regression and demonstrate the high utility of network-based machine learning for a better understanding of the spreading effects. By being able to predict the effect of a given individual being the patient zero, the proposed approach offers potentially orders of magnitude faster risk assessment and potentially aids the adopted epidemic spreading analysis techniques.

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.