Change Surfaces for Expressive Multidimensional Changepoints and Counterfactual Prediction

TL;DR

This paper introduces change surfaces as a flexible, multidimensional extension of changepoints, enabling complex, variable change detection and counterfactual prediction across multiple dimensions, demonstrated on large spatio-temporal datasets.

Contribution

It formalizes change surfaces, develops Gaussian Process Change Surfaces (GPCS), and introduces scalable methods for complex change detection and counterfactual analysis in high-dimensional data.

Findings

Discovered heterogeneous changes in measles incidence post-vaccine

Identified spatial and demographic patterns in lead testing requests

Demonstrated scalability and effectiveness of GPCS on large datasets

Abstract

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.