We live in the era of data deluge, where billions of gigabytes of data are generated and collected every day. Such a big amount of data has to be processed with the aim of improving our life in social, economic, scientific, medical aspects and more. Machine learning is a growing field that faces the challenges related to this ever-increasing data amount, like storage and processing, adversaries identification, denoising, time-variability, etc. Among several machine learning tools, graph-based methods are well-appreciated for their ability in capturing relevant information, recognizing patterns in a big amount of data, elaborate high dimensional signals or recover missing data. However, several existing approaches based on graphs are limited to tackle too ideal cases, where topology and/or signal perturbations are not considered. The present thesis aims at robustifying, against possible perturbations, learning tools used to accomplish several graph-learning tasks. In fact, in many cases, the graph underlying a network presents topology uncertainties/perturbations. A mismatch between the actual graph and the presumed one might be the result of the presence of graph topology inference errors, outliers, unexpected links failure, or model mismatch. One of the goals of this thesis is to analyze some graph signal processing tools taking into account topological perturbations. By incorporating any available prior knowledge on perturbations statistics, small perturbation theory of Laplacian matrices plays a key rule in our study. Small perturbation theory is instrumental also to accomplish the second goal of this thesis: Given a graph topology, we aim at identifying the edge whose perturbation causes the largest changes in the connectivity of the network. Then, we address two graph-based learning tasks in the presence of signal and topology perturbations. The first, is the topology identification tasks that may be affected by signal errors, due to outliers, adversaries or observation inaccuracy. To solve this problem, we rely on structural equation models, where signal errors may appear in both the input and output matrices. The second task that we analyze is the signal inference under topology perturbations. In both tasks, we develop total least squares approaches to take into account signal and/or topology perturbations. Finally, several numerical results show how perturbation-aware methods outperform classical methods that ignore possible perturbations.

Graph-based learning under model perturbations / Ceci, Elena. - (2020 Feb 18).

Graph-based learning under model perturbations

CECI, ELENA
18/02/2020

Abstract

We live in the era of data deluge, where billions of gigabytes of data are generated and collected every day. Such a big amount of data has to be processed with the aim of improving our life in social, economic, scientific, medical aspects and more. Machine learning is a growing field that faces the challenges related to this ever-increasing data amount, like storage and processing, adversaries identification, denoising, time-variability, etc. Among several machine learning tools, graph-based methods are well-appreciated for their ability in capturing relevant information, recognizing patterns in a big amount of data, elaborate high dimensional signals or recover missing data. However, several existing approaches based on graphs are limited to tackle too ideal cases, where topology and/or signal perturbations are not considered. The present thesis aims at robustifying, against possible perturbations, learning tools used to accomplish several graph-learning tasks. In fact, in many cases, the graph underlying a network presents topology uncertainties/perturbations. A mismatch between the actual graph and the presumed one might be the result of the presence of graph topology inference errors, outliers, unexpected links failure, or model mismatch. One of the goals of this thesis is to analyze some graph signal processing tools taking into account topological perturbations. By incorporating any available prior knowledge on perturbations statistics, small perturbation theory of Laplacian matrices plays a key rule in our study. Small perturbation theory is instrumental also to accomplish the second goal of this thesis: Given a graph topology, we aim at identifying the edge whose perturbation causes the largest changes in the connectivity of the network. Then, we address two graph-based learning tasks in the presence of signal and topology perturbations. The first, is the topology identification tasks that may be affected by signal errors, due to outliers, adversaries or observation inaccuracy. To solve this problem, we rely on structural equation models, where signal errors may appear in both the input and output matrices. The second task that we analyze is the signal inference under topology perturbations. In both tasks, we develop total least squares approaches to take into account signal and/or topology perturbations. Finally, several numerical results show how perturbation-aware methods outperform classical methods that ignore possible perturbations.
18-feb-2020
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1376043
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