With a rapid increase in volume and complexity of data sets, there is a need for methods that can extract useful information, for example the relationship between two data sets measured for the same persons. The Partial Least Squares (PLS) method can be used for this dimension reduction task. Within life sciences, results across studies are compared and combined. Therefore, parameters need to be identifiable, which is not the case for PLS. In addition, PLS is an algorithm, while epidemiological study designs are often outcome-dependent and methods to analyze such data require a probabilistic formulation. Moreover, a probabilistic model provides a statistical framework for inference. To address these issues, we develop Probabilistic PLS (PPLS). We derive maximum likelihood estimators that satisfy the identifiability conditions by using an EM algorithm with a constrained optimization in the M step. We show that the PPLS parameters are identifiable up to sign. A simulation study is conducted to study the performance of PPLS compared to existing methods. The PPLS estimates performed well in various scenarios, even in high dimensions. Most notably, the estimates seem to be robust against departures from normality. To illustrate our method, we applied it to IgG glycan data from two cohorts. Our PPLS model provided insight as well as interpretable results across the two cohorts.
Identifiability and Asymptotics in Learning Homogeneous Linear ODE Systems from Discrete Observations
University of Melbourne（墨尔本大学）；School of Mathematics and Statistics（数学与统计学院）；The University of Sydney（悉尼大学）；School of Computer Science（计算机科学学院）；Carnegie Mellon University（卡内基梅隆大学）；Mohamed bin Zayed University of Artificial Intelligence（穆罕默德·本·扎耶德人工智能大学）
SBI: A Simulation-Based Test of Identifiability for Bayesian Causal Inference
College of Information and Computer Sciences, University of Massachusetts, Amherst（马萨诸塞大学阿默斯特分校信息与计算机科学学院）；Basis Research Institute（贝西斯研究院）；Department of Brain and Cognitive Sciences, Massachusetts Institute of Technology（麻省理工学院脑与认知科学系）
