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.

翻译：许多研究收集的数据可被视为点过程的实现。这包括医学影像数据，其中伽马相机记录从注射伽马发射示踪剂的患者身上获得的光子计数。开发有助于诊断以及培训非专业放射科医师的分析方法具有重要意义。偏最小二乘法（PLS）是一种流行的分析方法，它结合了线性建模和降维的特点，以提供简洁的预测和分类。然而，现有的PLS方法不包括点过程预测变量的分析。在本文中，我们提出了点过程偏最小二乘法（P3LS），用于分析来自非齐次点过程集合的潜在时变强度函数。我们开发了一种新颖的$P^3LS$估计程序，该程序利用了对数高斯Cox过程的特性，并在模拟研究中检验了其经验性质。该方法被用于分析肾病患者的肾功能，以辅助诊断肾脏梗阻。