P3LS: Point Process Partial Least Squares

Many studies collect data that can be considered as a realization of a point process. Included are medical imaging data where photon counts are recorded by a gamma camera from patients being injected with a gamma emitting tracer. It is of interest to develop analytic methods that can help with diagnosis as well as in the training of inexpert radiologists. 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 (P3LS) for analyzing latent time-varying intensity functions from collections of inhomogeneous point processes. A novel estimation procedure for $P^3LS$ is developed that utilizes the properties of log-Gaussian Cox processes, and its empirical properties are examined in simulation studies. The method is used to analyze kidney functionality in patients with renal disease in order to aid in the diagnosis of kidney obstruction.