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Oberseminar WiSe 2011/12 Zusammenfassung des Vortrags von Franz Kiraly (TU Berlin)

Algebraische Geometrie im Machine Learning

Algebraic Geometry is increasingly gaining relevance in the applied sciences due to a growing number of problems which can be expressed in terms of real or complex algebra.

First of all, I will give a brief overview on recent applications of Algebraic Geometry and Computational Algebra, and then present my own research which revolves around the application of algebraic methods to exploit inherent structure of Machine Learning problems.

More specifically, I will exemplify this strategy by discussing an algorithm which uses Approximate Algebraic Geometry to solve a multidimensional statistical marginalization problem, and which has been successfully applied in the context of time series analysis. By a reformulation, the marginalization problem can be transformed in an algorithmic task related to general complete intersections in complex polynomial rings, which in turn can be tackled by new methods in Approximate Computational Algebra. On the other hand, the statistical problem can be studied via the algebraic properties of ideals generated by general elements.