2016/11/12 by Gilles Blanchard, Blanchard, Gilles, Nicole Mücke +1 · 1 citation
Mathematics · Decision Sciences · #Numerical methods in inverse problems #Statistical Methods and Inference #Probabilistic and Robust Engineering Design
paper · pdf · doi:10.48550/arxiv.1611.03979
We investigate if kernel regularization methods can achieve minimax\nconvergence rates over a source condition regularity assumption for the target\nfunction. These questions have been considered in past literature, but only\nunder specific assumptions about the decay, typically polynomial, of the\nspectrum of the the kernel mapping covariance operator. In the perspective of\ndistribution-free results, we investigate this issue under much weaker\nassumption on the eigenvalue decay, allowing for more complex behavior that can\nreflect different structure of the data at different scales.\n