Computational and statistical analysis of high throughput omics data, such as gene expressions, copy number alterations (CNAs), single nucleotide polymorphisms (SNPs) and DNA methylation (DNAm) has become very popular in cancer studies in recent decades because such analysis can be very helpful to predict whether a patient has certain disease or its subtypes. However, due to the high-dimensional nature of the data sets with hundreds of thousands of variables and very small numbers of samples, traditional machine learning approaches, such as Support Vector Machines (SVMs) and Random Forests (RFs), have limitations to analyze these data efficiently. In this thesis, we propose deep neural network (DNN) based models for classifying molecular subtypes of breast cancer and DNN-based regression models to account for interindividual variation in triglyceride concentrations measured at different visits of peripheral blood samples using epigenome-wide DNAm profiles.