  Scaling analysis, in which one infers scaling exponents and a scaling
function in a scaling law from given data, is a powerful tool for determining
universal properties of critical phenomena in many fields of science. However,
there are corrections to scaling in many cases, and then the inference problem
becomes ill-posed by an uncontrollable irrelevant scaling variable. We propose
a new kernel method based on Gaussian process regression to fix this problem
generally. We test the performance of the new kernel method for some example
cases. In all cases, when the precision of the example data increases,
inference results of the new kernel method correctly converge. Because there is
no limitation in the new kernel method for the scaling function even with
corrections to scaling, unlike in the conventional method, the new kernel
method can be widely applied to real data in critical phenomena.
