Professor Christian Grussler of the Faculty of Mechanical Engineering at Technion – Israel Institute of Technology, Israel, has visited CDSL. He gave an overview of his research on total positivity.
Prof. Grussler aims on developing the theory of total positivity in various areas, such as control theory, mathematical optimization, and machine learning. In the mentioned areas, smoothing operations are widely used: for example, smoothing filters for an output signal of a system or regularization terms in optimization problems, which smoothes the regression result and prevents overfitting. Prof. Grussler relates theses operations with the variation diminishing properties of matrices that have been studied in the classical total positivity theory. Briefly, a matrix is said to have a variation diminishing property if the number of sign changes of any vector decreases when it is multiplied with the matrix. In his recent paper, the properties of positive linear time-invariant systems are characterized in terms of positivity theory.
Since CDSL has been researching on Gaussian process regression (GPR) and its application to the control theory, there were questions on the relationship between GPR and total positivity. We thank prof. Grussler for sharing the great talk and we expect collaboration with CDSL in the near future.