Ioannidis, Vasileios2021-01-252021-01-252020-08https://hdl.handle.net/11299/218046University of Minnesota Ph.D. dissertation. August 2020. Major: Electrical Engineering. Advisor: Georgios Giannakis. 1 computer file (PDF); 126 pages.The era of "data deluge'' has sparked the interest in graph-based learning methods and their application in a number of disciplines ranging from sociology and biology to transportation or communications. Realizing the potential of graph-based learning has never been closer, even though formidable challenges are yet there to overcome. Contemporary graphs have massive scale up to billions of nodes, and generate unceasingly "big data''. Graph edges or node attributes may be only partially available due to application specific constraints, which calls for learning approaches to impute the missing information. Graph deep learning methods model complex nonlinear functions and achieve remarkable results in various tasks but the theoretical analysis of such methods is lacking. Last but not least, approaches to learning over graph data must be also robust to adversarial behavior. These challenges have been confronted only partly and separately under different formulations and application domains. The proposed research is centered on analytical and algorithmic foundations that aspire to address the aforementioned challenges facing robust deep learning tasks over large-scale dynamic graphs. The overarching vision is to leverage and adapt state-of-the-art deep learning, optimization and networking tools for inference tasks based on limited graph data. Target applications include identifying node and edge anomalies, predicting node attributes, as well as providing graph-driven recommendations. The ultimate goal is to both analytically and numerically demonstrate how valuable insights from {modeling graph data} can lead to markedly improved learning tools. To this end, the present thesis investigates three main research thrusts: i) unveiling anomalies on graphs; ii) robust deep learning on graphs; and iii) explaining deep learning on graphs via scattering transforms.The aforementioned research thrusts introduce novel methods that aim to tackle the challenges of robust deep learning on graphs. The potential of the proposed approaches is showcased by rigorous theoretical results and extensive experiments.enGraph neural networksGraphsMachine LearningNetwork scienceSupervised learningThesis or Dissertation