Graph Mining Methods for Predictive Toxicology

The graph structures of molecules can be a rich source of information about their biological activity or chemical reactivity – however, very efficient methods are required for analyzing them. Due to its complexity, any representation of a chemical database can only convey some characteristics of the whole graph corpus. Additionally, the interesting patterns emerge only from the whole set of graphs that constitute the database, not from individual ones, which places a demand for timeand memory-efficient algorithms. A primary goal of graph mining is to find subgraphs that occur with a certain frequency in a given dataset. The amount of such patterns is usually enormous for chemical structure graphs, even when additional filters are employed, such as restricting the result set to subgraphs that primarily occur in the toxic or non-toxic compounds. Therefore, the patterns can often not be used directly for predictive modeling, since they would overfit and/or place a high load on learning algorithms, while at the same time provide a much too fine-grained information to experts. More concise representations would have a significant value to the user, even if more time was needed to calculate them. Concise representations may be obtained, for example, by compression of the pattern set, or lifted representations of molecular fragments. This work shows that such representations may be obtained efficiently in practice, and that they can be of considerable utility for predictive models. It presents a set of algorithmic tools for the extraction of interesting subgraphs and subgraph patterns from molecular databases, and reports on experiments that assess their utility in the context of predictive models. For discovering the most expressive patterns, a combination of structural and statistical constraints is employed. The structural constraints make use of the partial order, in which subgraphs can be put, and on which a refinement operator can be defined. The statistical constraints have the convexity property, allowing for efficient search in combination with the structural constraints. While the approaches are not restricted to chemical structures and toxicological databases, I find the problem of graph mining particularly compelling in this domain, because there has been a rapidly increasing need for efficient and precise computational models in chemical risk assessment during the last decade.