Variable Selection and Classification for Longitudinal Binary Data Through Three-Step Sparse Boosting

Emer, Deniz Esin
With the rapid evolution of technology, it is now possible to obtain the gene expression levels of thousands of genes in a single experiment. In these experiments, the sample size is relatively small but the number of covariates under consideration is extremely large, whereas only a small number of expressions may be related to the outcome of interest. Hence, the selection of causal features is much-needed along with the model estimation. In this thesis, we propose a three-step sparse boosting model for detecting the most important covariates that classify the individuals into binary groups considering the longitudinal data having spatial and temporal correlations. Following the idea of Yue, Li and Cheng (2019), in the first step, the independence of the observations is assumed and the estimation of coefficients of logistic regression is obtained by directly minimizing the binary-cross entropy loss using boosting method. Then, in the second step, the temporal correlation is considered by executing a weight matrix constructed based on the errors made in the first step. Finally, in the third step, the spatial correlation is added via a weight matrix considering the correlation structure. A Monte Carlo Simulation Study was designed and nine different temporal and spatial correlation structure scenario were run using parallel computing methods. The proposed model decreased the number of mistakenly chosen significant covariates while establishing all the true ones as significant. As the classification performance, it got higher when the spatial and temporal correlations got higher. Also, a comparison study, including Boruta (RF), Support Vector Machine (SVM), Logistic Regression, Ridge Regression, Lasso Regression and Elastic Net algorithms, showed that i) they considered very large number of mistakenly chosen significant covariates, whereas our proposed algorithm identified at most one along with the true significant variables and, ii) Three-Step Sparse Boosting algorithm performs the best in terms of specificity and precision metrics in the simulation study. In addition, the algorithm had been applied on a real life data set of Type 1 Diabetes Prediction and Prevention (DIPP) study, using both balanced and unbalanced sets. Our algorithm identified a few numbers of genes as significant which can be beneficial regarding time and money. The comparison results showed that The Three-Step Sparse Boosting technique can be considered as performing well in terms of variable selection, estimation and classification.


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Citation Formats
D. E. Emer, “Variable Selection and Classification for Longitudinal Binary Data Through Three-Step Sparse Boosting,” Ph.D. - Doctoral Program, Middle East Technical University, 2022.