Emanuel Hedberg: Maskininlärning med linjära system

Abstract: This thesis explores some of the underlying mathematics behind machine learning, with a focus on linear algebra, especially Sylvester equations. These equations make appearances in areas such as control theory, but also even in machine learning contexts, such as weight-initialization, image processing, or multi-label learning. Research has shown how some optimization or labeling problems can be reduced to solving a Sylvester equation. Moreover, this thesis goes into both numerical methods of solving these equations as well as the necessary preconditions which guarantee a unique solution, with accompanying proof.