Accuracy versus interpretability in exible modeling : implementing a tradeo using Gaussian process modelsTony

One of the widely acknowledged drawbacks of exible statistical models is that the tted models are often extremely diicult to interpret. However, if exible models are constrained to be additive the tted models are much easier to interpret, as each input can be considered independently. The problem with additive models is that they cannot provide an accurate model if the phenomenon being modeled is not additive. This paper shows that a tradeoo between accuracy and additivity can be implemented easily in Gaussian process models, which are a type of exible model closely related to feedforward neural networks. One can t a series of Gaussian process models that begins with the completely exible and are constrained to be progressively more additive, and thus progressively more interpretable. Observations of how the degree of non-additivity and the test error change as the models become more additive give insight into the importance of interactions in a particular model. Fitted models in the series can also be interpreted graphically with a technique for visualizing the eeects of inputs in non-additive models that was adapted from plots for generalized additive models. This visualization technique shows the overall eeects of diierent inputs and also shows which inputs are involved in interactions and how strong those interactions are.