Browsing by Author "Ioannidis, Vasileios"
Now showing 1 - 2 of 2
Results Per Page
Sort Options
Item Kernel-based Reconstruction of Dynamic Functions over Dynamic Graphs(2017-08) Ioannidis, VasileiosGraph-based methods pervade the inference toolkits of numerous disciplines including sociology, biology, neuroscience, physics, chemistry, and engineering. A challenging problem encountered in this context pertains to determining the attributes of a set of vertices given those of another subset at possibly dierent time instants. Leveraging spatiotemporal dynamics and prior information can drastically reduce the number of observed vertices, and hence the cost of sampling. Alleviating the limited exibility of existing approaches, this thesis broadens the kernel-based graph function estimation framework to reconstruct time-evolving functions over possibly time-evolving topologies. This encompassing approach inherits the versatility and generality of kernel-based methods, for which no knowledge on distributions or second-order statistics is required. Ecient inference algorithms are derived that operate in an online and even data-adaptive fashion. Moreover, semi-parametric approaches capable of incorporating the structure of known graph functions without sacri- cing the exibility of the overall model are advocated. Numerical tests with real data sets corroborate the merits of the proposed methods relative to competing alternatives.Item Robust Deep Learning on Graphs(2020-08) Ioannidis, VasileiosThe 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.