Bizonytalan konvex optimalizálás a gépi tanulásban

Témavezető:	Csáji Balázs Csanád
	SZTAKI és ELTE TTK Valószínűségelméleti és Statisztika Tanszék
email:	csaji@sztaki.hu

Projekt leírás

Convex optimization arises in several machine learning methods, especially in supervised learning. Typical examples which lead to various convex programs are support vector machines (classification and regression) that are fundamental tools of statistical learning theory. The resulting optimization problems depend on the data, which are typically assumed be (i.i.d.) random samples from an unknown probability distribution. In order to study the risk and generalization capabilities of the obtained models, we should take the uncertainty of the data into account. The project aims at investigating recent advances in the theory of scenario-based (uncertain) convex optimization and studying their implications for statistical learning methods.

Előfeltételek

• Szükséges nyelvtudás: angol
• Programozási ismeretek: Python vagy Matlab

Hivatkozások

• Boyd, S. & Vandenberghe, L. (2004): Convex Optimization. Cambridge University Press
• Campi, M. C., & Garatti, S. (2018): Introduction to the Scenario Approach. SIAM: Society for Industrial and Applied Mathematics
• Campi, M. C. & Garatti, S. (2021): A Theory of the Risk for Optimization with Relaxation and its Application to Support Vector Machines. Journal of Machine Learning Research (JMLR). 22: 288:1-288:38

Korábbi hallgatók

• Ivkovic Iván: Uncertain Convex Optimization in Machine Learning (2019/20 I. félév Önálló projekt, szakmai gyakorlat I)
• Ivkovic Iván: Uncertain Convex Optimization in Machine Learning (2019/20 II. félév Önálló projekt, szakmai gyakorlat II)