Regularised Least-Squares Regression with Infinite-Dimensional Output Space
This work addresses theoretical foundations for regression in infinite-dimensional output spaces, but it is incremental as it focuses on minimal assumptions without optimizing rates or constants.
The paper tackles the problem of vector-valued reproducing kernel Hilbert space regression with non-compact input and infinite-dimensional output spaces, using integral operator techniques and spectral theory to derive learning theory results with minimal assumptions, such as relying only on Chebyshev's inequality.
This short technical report presents some learning theory results on vector-valued reproducing kernel Hilbert space (RKHS) regression, where the input space is allowed to be non-compact and the output space is a (possibly infinite-dimensional) Hilbert space. Our approach is based on the integral operator technique using spectral theory for non-compact operators. We place a particular emphasis on obtaining results with as few assumptions as possible; as such we only use Chebyshev's inequality, and no effort is made to obtain the best rates or constants.