Renata Wong

Nan-Hong Kuo, Renata Wong

We establish a mathematical equivalence between Support Vector Machine (SVM) kernel functions and quantum propagators represented by time-dependent Green's functions, which has remained largely unexplored. We demonstrate that many common SVM kernels correspond naturally to Green's functions via operator inversion theory. The sigmoid kernel does not always satisfy Mercer's theorem, and therefore the corresponding Green's function may also fail to perform optimally. We further introduce a Kernel Polynomial Method (KPM) for designing customized kernels that align with Green's functions. Our numerical experiments confirm that employing positive-semidefinite kernels that correspond to Green's functions significantly improves predictive accuracy of SVM models in physical systems.

Renata Wong

Abstract argumentation frameworks are formal systems that facilitate obtaining conclusions from non-monotonic knowledge systems. Within such a system, an argumentation semantics is defined as a set of arguments with some desired qualities, for example, that the elements are not in conflict with each other. Splitting an argumentation framework can efficiently speed up the computation of argumentation semantics. With respect to stable semantics, two methods have been proposed to split an argumentation framework either in a unidirectional or bidirectional fashion. The advantage of bidirectional splitting is that it is not structure-dependent and, unlike unidirectional splitting, it can be used for frameworks consisting of a single strongly connected component. Bidirectional splitting makes use of a minimum cut. In this paper, we implement and test the performance of the bidirectional splitting method, along with two types of graph cut algorithms. Experimental data suggest that using a minimum cut will not improve the performance of computing stable semantics in most cases. Hence, instead of a minimum cut, we propose to use a balanced cut, where the framework is split into two sub-frameworks of equal size. Experimental results conducted on bidirectional splitting using the balanced cut show a significant improvement in the performance of computing semantics.