Spectral Analysis of Symmetric and Anti-Symmetric Pairwise Kernels
This work addresses a theoretical gap in kernel methods for structured data, but it appears incremental as it builds on existing symmetrization techniques with analytical extensions.
The paper tackles the problem of learning regression functions from pairwise data with symmetry or anti-symmetry constraints by analyzing how symmetrizing or anti-symmetrizing kernel functions reduces effective dimension and bounds regularization bias.
We consider the problem of learning regression functions from pairwise data when there exists prior knowledge that the relation to be learned is symmetric or anti-symmetric. Such prior knowledge is commonly enforced by symmetrizing or anti-symmetrizing pairwise kernel functions. Through spectral analysis, we show that these transformations reduce the kernel's effective dimension. Further, we provide an analysis of the approximation properties of the resulting kernels, and bound the regularization bias of the kernels in terms of the corresponding bias of the original kernel.