This book covers the recent advancement of statistical methods for the analysis of longitudinal data. Real datasets from four large NIH-supported longitudinal clinical trials and epidemiological studies illustrate the practical applications of the statistical methods. This book focuses on the nonparametric approaches, which have gained tremendous popularity in biomedical studies. These approaches have the flexibility to answer many scientific questions that cannot be properly addressed by the existing parametric approaches, such as the linear and nonlinear mixed effects models.

Longitudinal studies, which involve repeated observations, taken at irregularly spaced time points, for a set of individuals over time, are ubiquitous in many applications. Predictive models for longitudinal data generally need to take into account the data correlation, i.e., correlation among repeated observations of the individual and/or correlation among groups of individuals. Ignoring either part of the correlation can lead to misleading statistical inferences. It can be non-trivial to choose a suitable correlation structure that reflects the correlations present in the data. The relationships between the variables and outcomes of interest can be highly complex and non-linear. Furthermore, modern applications often call for longitudinal methods that scale gracefully with increasing number of variables and millions of data points. The target for this dissertation is to address the challenges in longitudinal data analysis using machine learning and representation learning approaches. Specifically, our work is dedicated to redesign the state-of-the-art longitudinal models to fit in the large-scale, high-dimensional longitudinal settings. We focus on improving the mixed effects models and non-parametric models by answering the following research questions: (i) How can we design mixed effects models to handle longitudinal data with thousands of variables and automate the selection between fixed and random effects? (ii) How can we design non-parametric models to handle longitudinal data with time-varying and time-invariant effects and automate the discovery of complex correlation? (iii) How can we design non-parametric models to handle longitudinal data with outcomes that could show state transitions, abrupt discontinuities and complex correlation? Against this background, this dissertation investigates two lines of approaches, Factorization Machines and Gaussian Process. We tackle both the theoretical and practical challenges in adapting these approaches to longitudinal settings. For each proposed model, we explore provably efficient algorithm to improve its applicability over high-dimensional data.

Rcpp is the glue that binds the power and versatility of R with the speed and efficiency of C++. With Rcpp, the transfer of data between R and C++ is nearly seamless, and high-performance statistical computing is finally accessible to most R users. Rcpp should be part of every statistician's toolbox. -- Michael Braun, MIT Sloan School of Management "Seamless R and C++ integration with Rcpp" is simply a wonderful book. For anyone who uses C/C++ and R, it is an indispensable resource. The writing is outstanding. A huge bonus is the section on applications. This section covers the matrix packages Armadillo and Eigen and the GNU Scientific Library as well as RInside which enables you to use R inside C++. These applications are what most of us need to know to really do scientific programming with R and C++. I love this book. -- Robert McCulloch, University of Chicago Booth School of Business Rcpp is now considered an essential package for anybody doing serious computational research using R. Dirk's book is an excellent companion and takes the reader from a gentle introduction to more advanced applications via numerous examples and efficiency enhancing gems. The book is packed with all you might have ever wanted to know about Rcpp, its cousins (RcppArmadillo, RcppEigen .etc.), modules, package development and sugar. Overall, this book is a must-have on your shelf. -- Sanjog Misra, UCLA Anderson School of Management The Rcpp package represents a major leap forward for scientific computations with R. With very few lines of C++ code, one has R's data structures readily at hand for further computations in C++. Hence, high-level numerical programming can be made in C++ almost as easily as in R, but often with a substantial speed gain. Dirk is a crucial person in these developments, and his book takes the reader from the first fragile steps on to using the full Rcpp machinery. A very recommended book! -- Søren Højsgaard, Department of Mathematical Sciences, Aalborg University, Denmark "Seamless R and C ++ Integration with Rcpp" provides the first comprehensive introduction to Rcpp. Rcpp has become the most widely-used language extension for R, and is deployed by over one-hundred different CRAN and BioConductor packages. Rcpp permits users to pass scalars, vectors, matrices, list or entire R objects back and forth between R and C++ with ease. This brings the depth of the R analysis framework together with the power, speed, and efficiency of C++. Dirk Eddelbuettel has been a contributor to CRAN for over a decade and maintains around twenty packages. He is the Debian/Ubuntu maintainer for R and other quantitative software, edits the CRAN Task Views for Finance and High-Performance Computing, is a co-founder of the annual R/Finance conference, and an editor of the Journal of Statistical Software. He holds a Ph.D. in Mathematical Economics from EHESS (Paris), and works in Chicago as a Senior Quantitative Analyst.