  Identifying changes in model parameters is fundamental in machine learning
and statistics. However, standard changepoint models are limited in
expressiveness, often addressing unidimensional problems and assuming
instantaneous changes. We introduce change surfaces as a multidimensional and
highly expressive generalization of changepoints. We provide a model-agnostic
formalization of change surfaces, illustrating how they can provide variable,
heterogeneous, and non-monotonic rates of change across multiple dimensions.
Additionally, we show how change surfaces can be used for counterfactual
prediction. As a concrete instantiation of the change surface framework, we
develop Gaussian Process Change Surfaces (GPCS). We demonstrate counterfactual
prediction with Bayesian posterior mean and credible sets, as well as massive
scalability by introducing novel methods for additive non-separable kernels.
Using two large spatio-temporal datasets we employ GPCS to discover and
characterize complex changes that can provide scientific and policy relevant
insights. Specifically, we analyze twentieth century measles incidence across
the United States and discover previously unknown heterogeneous changes after
the introduction of the measles vaccine. Additionally, we apply the model to
requests for lead testing kits in New York City, discovering distinct spatial
and demographic patterns.

Machine Learning;Artificial Intelligence;Machine Learning;Methodology