Projektbeschreibung
Algorithmen für die Auswertung hochdimensionaler Daten
Mit fortschrittlichen Computertechnologien können immense Datenmengen erfasst und gespeichert werden. In vielen wissenschaftlichen Gebieten, in denen die Daten und das maschinelle Lernen hochdimensional sind, ist es zunehmend schwierig, Daten auszuwerten und mit konventionellen Statistiktheorien genaue Schlüsse zu ziehen. Das ist besonders in der Medizin eine Herausforderung. Daher wird im ERC-finanzierten Projekt INF_2 ein theoretischer Rahmen zur hochdimensionalen Auswertung beim maschinellen Lernen und in der Datenwissenschaft aufgestellt. Anhand der Molekularfeldtheorie werden die grundlegenden Grenzen, oder Mindestdatenanforderungen, der Inferenz bestimmt und Algorithmen erarbeitet, die mit dieser minimalen Datenmenge effektiv funktionieren. Die Grundsätze werden dann an reale Anwendungen in genomweiten Assoziationsstudien angepasst.
Ziel
Extracting information from data is the key challenge of our time, and in many applications (e.g. genome-wide association studies, data compression, and virtual assistants such as ChatGPT) both the data and the machine learning model used to extract information are increasingly high-dimensional. As traditional statistical theory is ill-equipped to face this explosion in the dimensionality of the problem, machine learning is now predominantly experimental. However, empirical approaches come with huge costs affordable only to large companies, and they lack interpretability, which is especially troublesome in medical applications. To address these issues, the INF^2 project develops information-theoretically principled methods for high-dimensional inference in machine learning and data science. The key insight is that, via a “mean-field” approach, high-dimensional quantities are well approximated by low-dimensional ones and then characterized exactly. Leveraging this characterization, we will (i) establish the fundamental limits of inference, i.e. the minimal amount of data necessary to solve the problem, and (ii) design efficient algorithms requiring only the minimal amount of data. The challenge we tackle is to apply this paradigm to practical settings, in which data are structured and heterogeneous (as in genome-wide association studies), and models consist of complex architectures tailored to applications (auto-encoders for data compression, and transformers for ChatGPT). Through a novel analysis of spectral methods, approximate message passing and gradient descent, INF^2 builds a theoretical framework having conceptual impact, as well as vast applicability, in machine learning and information theory. This framework is then brought to the real world via applications in genome-wide association studies. Broadly, our results enable the principled design of machine learning algorithms and models, drastically reducing costs and providing interpretable solutions.
Schlüsselbegriffe
Programm/Programme
- HORIZON.1.1 - European Research Council (ERC) Main Programme
Thema/Themen
Finanzierungsplan
HORIZON-ERC - HORIZON ERC GrantsGastgebende Einrichtung
3400 Klosterneuburg
Österreich