Projektbeschreibung
Den Sinn komplexer Daten und Zusammenhänge verstehen
Um die Welt um uns herum besser zu verstehen, werden dringend Modelle gebraucht. Sind sie erst einmal entwickelt, können wir Parameter ändern, um Hypothesen zu prüfen und mögliche Ergebnisse zu bewerten. Jedoch beruht die Konstruktion von Modellen teilweise auf Beobachtungen, aus denen wir bestimmte „Regeln“ oder Verhaltensweisen, mathematische Beschreibungen von Beziehungen ableiten, welche die Algorithmen der Modelle selbst bilden. Deshalb kann die Wiederherstellung der „Struktur“ von Daten eine äußerst komplizierte Aufgabe sein. Das EU-finanzierte Projekt SO-ReCoDi wird robuste Wiederherstellungsalgorithmen entwickeln, die mithilfe der Vereinheitlichung mehrerer moderner Verfahren auf einige schwierige Probleme anwendbar sein werden.
Ziel
In a recovery problem, we are interested in recovering structure from data that contains a mix of combinatorial structure and random noise. In a robust recovery problem, the data may contain adversarial perturbations as well. A series of recent results in theoretical computer science has led to algorithms based on the convex optimization technique of Semidefinite Programming for several recovery problems motivated by unsupervised machine learning. Can those algorithms be made robust? Sparsifiers are compressed representations of graphs that speed up certain algorithms. The recent proof of the Kadison-Singer conjecture by Marcus, Spielman and Srivastava (MSS) shows that certain kinds of sparsifiers exist, but the proof does not provide an explicit construction. Dynamics and population protocols are simple models of distributed computing that were introduced to study sensor networks and other lightweight distributed systems, and have also been used to model naturally occurring networks. What can and cannot be computed in such models is largely open. We propose an ambitious unifying approach to go beyond the state of the art in these three domains, and provide: robust recovery algorithms for the problems mentioned above; a new connection between sparsifiers and the Szemeredi Regularity Lemma and explicit constructions of the sparsifiers resulting from the MSS work; and an understanding of the ability of simple distributed algorithms to solve community detection problems and to deal with noise and faults. The unification is provided by a common underpinning of spectral methods, random matrix theory, and convex optimization. Such tools are used in technically similar but conceptually very different ways in the three domains. By pursuing these goals together, we will make it more likely that an idea that is natural and simple in one context will translate to an idea that is deep and unexpected in another, increasing the chances of a breakthrough.
Wissenschaftliches Gebiet
Programm/Programme
Thema/Themen
Finanzierungsplan
ERC-ADG - Advanced GrantGastgebende Einrichtung
20136 Milano
Italien