Connecting actuarial judgment to probabilistic learning techniques with graph theory

The aim of improvements in data driven exercises in insurance has led to the desire to gather additional data than traditionally available. In addition to underwriting characteristics such as age, gender and address, technology now allows the collection of many more variables. Examples include dynamic data from sensors for driving behaviour in vehicles, appliance and electrical usage in homes and static data from external databases on traffic violations, crime scores or credit scores. High dimensional models arise if modelling sensor data at multiple time points and the individual variables that comprise summary scores. Reasoning with a large number of variables can become unnecessarily complex without any actuarial judgment. For example, it may not be necessary to include hundreds of rating factors as predictors if many of them are known to be related or unnecessary. This discussion proposes the use of graph theory as a means of translating intuitive reasoning to mathematical properties. This is done via graphical models, which involve the use of graph theory to formulate probabilistic models (Lauritzen, 1996). The approach has been used in applications such as medical expert systems (Franklin et al., 1989), natural language processing (Blei et al., 2003), image processing, bioinformatics and others (Wainwright and Jordan, 2008).