  We study kernel quadrature rules with convex weights. Our approach combines
the spectral properties of the kernel with recombination results about point
measures. This results in effective algorithms that construct convex quadrature
rules using only access to i.i.d. samples from the underlying measure and
evaluation of the kernel and that result in a small worst-case error. In
addition to our theoretical results and the benefits resulting from convex
weights, our experiments indicate that this construction can compete with the
optimal bounds in well-known examples.
