Signal Processing and Information Extraction, from Data to Complex Models and Structures

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This research focuses on statistical learning of complex systems and structures in presence of large scale data. Our increasing ability to collect massive volumes of data demands an urgent need for analysis, interpretation, and modeling of the underlying structures of these collected data which is the main motivation of this work. Trustworthy data modeling becomes vital especially in scenarios where the use of unreliable model can cause irreversible damages. Examples of such cases are actions based on various health sector data analysis and environmental decisions based on conclusions from large collected data. Despite advantages of our ability in storing the “big” data, they also come with inherent “big” challenges for proper information extraction. Huge data set size, in both cardinality and member dimension, requires extracting lower dimension informative data in real applications. Much of research in this area is now dedicated to data sketching through approaches such as development of efficient tensor analysis and/or design of adaptive kernel functions. These data modeling methods are heavily sensitive to the inevitable dimension reduction process. The recent modeling approaches for large scale data take advantages of including latent variables in the parametric modeling. For example, one popular approach in this direction is deep learning. While these methods are quite successful with noise removal on the large data sets, issues such as uncertainty in labeling, overfitting, and verification of convergence to the true model are extremely important in these approaches. In addition, in all the research trends for large data modeling, simultaneous complexity analysis and robust performance are critical tasks in various machine learning methods such as data clustering, classification, compression, and predictive structural modeling. The main concentration of this project is on these important challenges of large data modeling. It will focus on validation approaches for structural data modeling, complexity analysis, and optimum choice of number of parameters in modeling. As more data becomes available, the modeling methods have the luxury of becoming more complex with higher number of parameters. The crucial challenge, however, is that the rate of growth in modeling complexity has to be monitored such that it can guarantee providing more precise modeling and doesn't lose reliability by overfitting. The intended outcome of this research provides theory, knowledge, and algorithms for feasible data-driven structural modeling. Immediate impact of the project is in developing efficient, reliable, and most importantly verifiable methods of structural data modeling.