Learning Models For Corrupted Multi-Dimensional Data: Fundamental Limits And Algorithms

LEARNING MODELS FOR CORRUPTED MULTI-DIMENSIONAL DATA: FUNDAMENTAL LIMITS AND ALGORITHMS by ISHAN JINDAL May 2019 Advisors: Dr. Harpreet Singh and Dr. Matthew Nokleby Major: Electrical and Computer Engineering Degree: Doctor of Philosophy The development of machine learning models that can handle corrupted data, such as training data with unreliable labels or multi-dimensional signals corrupted by noise or data erasures, have become a central necessity in the era of learning from massive datasets. Large datasets are typically generated via human annotation, which results in human errors that cannot be eliminated at scale. Existing techniques for dealing with noisy datasets do not exploit the multi-dimensional structures of the signals, which could be used to improve the overall classification and representation performance of the model. In this thesis, we develop a Kronecker-structure (K-S) subspace model that exploits the multi-dimensional structure of the signal. First, we study the classification performance of K-S subspace models in two asymptotic regimes when the signal dimensions go to infinity and when the noise power tends to zero. We characterize the misclassification probability in terms of diversity order and we drive an exact expression for the diversity order. We further derive a tighter bound on misclassification probability in terms of pairwise geometry of the subspaces. The proposed scheme is optimal in most of the signal dimension regimes except in one regime where the signal dimension is less than twice the subspace dimension,