Sparse Model Selection using Information Complexity

This dissertation studies and uses the application of information complexity to statistical model selection through three different projects. Specifically, we design statistical models that incorporate sparsity features to make the models more explanatory and computationally efficient.

In the first project, we propose a Sparse Bridge Regression model for variable selection when the number of variables is much greater than the number of observations if model misspecification occurs. The model is demonstrated to have excellent explanatory power in high-dimensional data analysis through numerical simulations and real-world data analysis.

The second project proposes a novel hybrid modeling method that utilizes a mixture of sparse principal component regression (MIX-SPCR) to segment high-dimensional time series data. Using the MIX-SPCR model, we empirically analyze the S\&P 500 index data (from 1999 to 2019) and identify two key change points.

The third project investigates the use of nonlinear features in the Sparse Kernel Factor Analysis (SKFA) method to derive the information criterion. Using a variety of wide datasets, we demonstrate the benefits of SKFA in the nonlinear representation and classification of data. The results obtained show the flexibility and the utility of information complexity in such data modeling problems.