P3LS: Point Process Partial Least Squares.

Many studies collect data that can be considered as a realization of a point process. Partial least squares (PLS) is a popular analytic approach that combines features from linear modeling as well as dimension reduction to provide parsimonious prediction and classification. However, existing PLS methodologies do not include the analysis of point process predictors. In this article, we introduce point process PLS ($P^3LS$) for analyzing latent time-varying intensity functions from collections of inhomogeneous point processes. We develop a novel estimation procedure for $P^3LS$ that utilizes the properties of log-Gaussian Cox processes and examine its empirical properties via simulation studies. In addition, we establish the predictive consistency for the $P^3LS$. Finally, we apply the proposed method to a renal radionuclide imaging study to predict kidney obstruction from patient renograms. The method yields a clinically meaningful and interpretable model, demonstrating its potential to support data-driven clinical decision-making in renal studies.