Public defence in Signal Processing Technology, M.Sc. Emadaldin Mozafari Majd

The title of the thesis: Statistically Robust and Sparsity Promoting Inference and Estimation for Large-Scale Data

Thesis defender: Emadaldin Mozafari Majd
Opponent: Prof. Dr. Michael Muma, TU Darmstadt, Germany
Custos: Prof. Visa Koivunen, Aalto University School of Electrical Engineering, Department of Information and Communications Engineering 

With datasets expanding in volume and dimensionality, many traditional procedures in signal processing, statistics, and machine learning face difficulties such as high computational complexity, lack of robustness, and reduced statistical performance. Furthermore, the probability of having missing and outlying data points grows when observing large-scale data, which further complicates estimation and inference tasks. The realization of sophisticated inference and estimation procedures that are compatible with distributed computing architectures, robust against outlying data points, and maintain reliable or even optimal statistical performance when sample size, dimensionality, or both grow is of paramount importance. 

This dissertation addresses two commonly arising problems in the analysis of large-scale data, which are possibly high-dimensional. It introduces new contributions in terms of theory and algorithms to the fields of inference and estimation. First, we develop two-stage robust and distributed statistical inference procedures for sparse linear regression models, backed by new theoretical guarantees on robustness and asymptotic behavior. Second, we introduce a new regularization-based estimator for high-dimensional sparse linear models in the face of heavy-tailed distributions and outlying data points, which possesses desirable oracle and robustness properties. These findings provide valuable tools for modern large-scale data analysis, particularly in scenarios with data perturbations and model misspecifications.

Thesis available for public display 10 days prior to the defence at: https://aaltodoc.aalto.fi/doc_public/eonly/riiputus/

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Doctoral theses in the School of Electrical Engineering: https://aaltodoc.aalto.fi/handle/123456789/53