  The choice of parameters in neural networks is crucial in the performance,
and an oracle distribution derived from the ridgelet transform enables us to
obtain suitable initial parameters. In other words, the distribution of
parameters is connected to the integral representation of target functions. The
oracle distribution allows us to avoid the conventional backpropagation
learning process; only a linear regression is enough to construct the neural
network in simple cases. This study provides a new look at the oracle
distributions and ridgelet transforms, i.e., an aspect of importance sampling.
In addition, we propose extensions of the parameter sampling methods. We
demonstrate the aspect of importance sampling and the proposed sampling
algorithms via one-dimensional and high-dimensional examples; the results imply
that the magnitude of weight parameters could be more crucial than the
intercept parameters.
