Prediction of Spatial Point Processes: Regularized Method with Out-of-Sample Guarantees
This addresses the challenge of reliable spatial prediction for applications like environmental monitoring or epidemiology, offering a robust solution with theoretical guarantees, though it appears incremental as it builds on regularization techniques.
The paper tackles the problem of predicting spatial point processes by developing a method to infer predictive intensity intervals using a regularized criterion, and proves that it provides out-of-sample performance guarantees even under model misspecification, as demonstrated on synthetic and real data.
A spatial point process can be characterized by an intensity function which predicts the number of events that occur across space. In this paper, we develop a method to infer predictive intensity intervals by learning a spatial model using a regularized criterion. We prove that the proposed method exhibits out-of-sample prediction performance guarantees which, unlike standard estimators, are valid even when the spatial model is misspecified. The method is demonstrated using synthetic as well as real spatial data.