Ph.D Thesis Defense: "Smooth ICA Model and Multi-Level ICA Model under Assumptions of Time Pattern"

Abstract: Independent component analysis (ICA) is wildly used in differently areas. As traditional ICA models make no assumption on time patterns, they do not take time domain information into consideration. We introduced new assumptions that allow local dependence over time, and built smooth ICA models to utilize the smoothness information for sources signals. Based on the local dependence assumptions, smooth ICA estimators using smoothness penalty in constrained optimization were introduced, with proofs about the consistency and asymptotic normality of such estimators. We then derived the Newton iterative update to solve for smooth ICA estimators, and formulated the complete smooth ICA algorithms in detials. Performance of smooth ICA on Monte Carlo simulations, and on real fMRI datasets was also discussed. We also discussed the ICA settings on multiple subjects dataset, and proposed new multi-level ICA model and algorithm. Then simulation results were discussed for this model.

Host: Jimin Ding