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Identifying changes in model parameters is fundamental in machine learningand statistics. However, standard changepoint models are limited inexpressiveness, often addressing unidimensional problems and assuminginstantaneous changes. We introduce change surfaces as a multidimensional andhighly expressive generalization of changepoints. We provide a model-agnosticformalization 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 counterfactualprediction. As a concrete instantiation of the change surface framework, wedevelop Gaussian Process Change Surfaces (GPCS). We demonstrate counterfactualprediction with Bayesian posterior mean and credible sets, as well as massivescalability by introducing novel methods for additive non-separable kernels.Using two large spatio-temporal datasets we employ GPCS to discover andcharacterize complex changes that can provide scientific and policy relevantinsights. Specifically, we analyze twentieth century measles incidence acrossthe United States and discover previously unknown heterogeneous changes afterthe introduction of the measles vaccine. Additionally, we apply the model torequests for lead testing kits in New York City, discovering distinct spatialand demographic patterns.

Change Surfaces for Expressive Multidimensional Changepoints and Counterfactual Prediction