Predictions and learning with random monomial ideals

  • Robert Krone (University of California, Davis, Davis, USA)
E1 05 (Leibniz-Saal)


Many computational problems on polynomial ideals are known to have bad worst-case running times. Can we instead make a quick probabilistic guess at the answer? One strategy is to understand what properties are very likely to occur in a given random model. As the degree of the generators grow, we asymptotically almost surely predict projective dimension and Cohen-Macaulayness of monomial ideals, adding to previous work on Krull dimension. Another approach is to use machine learning to allow a computer to make predictions. We train neural networks to estimate Krull dimension and projective dimension of monomial ideals with good accuracy. This is joint work with Jesus de Loera, Serkan Hosten, Lily Silverstein, and Zekai Zhao.

01.07.19 04.07.19

Summer School on Randomness and Learning in Non-Linear Algebra

MPI für Mathematik in den Naturwissenschaften Leipzig (Leipzig) E1 05 (Leibniz-Saal)
Universität Leipzig (Leipzig) Felix-Klein-Hörsaal

Saskia Gutzschebauch

Max-Planck-Institut für Mathematik in den Naturwissenschaften Contact via Mail

Paul Breiding

Technische Universität Berlin

Jesus De Loera

University of California at Davis

Despina Stasi

Illinois Institute of Technology

Sonja Petrovic

Illinois Institute of Technology