  The density estimation is one of the core problems in statistics. Despite
this, existing techniques like maximum likelihood estimation are
computationally inefficient due to the intractability of the normalizing
constant. For this reason an interest to score matching has increased being
independent on the normalizing constant. However, such estimator is consistent
only for distributions with the full space support. One of the approaches to
make it consistent is to add noise to the input data which is called Denoising
Score Matching. In this work we derive analytical expression for the Denoising
Score matching using the Kernel Exponential Family as a model distribution. The
usage of the kernel exponential family is motivated by the richness of this
class of densities. To tackle the computational complexity we use Random
Fourier Features based approximation of the kernel function. The analytical
expression allows to drop additional regularization terms based on the
higher-order derivatives as they are already implicitly included. Moreover, the
obtained expression explicitly depends on the noise variance, so the validation
loss can be straightforwardly used to tune the noise level. Along with
benchmark experiments, the model was tested on various synthetic distributions
to study the behaviour of the model in different cases. The empirical study
shows comparable quality to the competing approaches, while the proposed method
being computationally faster. The latter one enables scaling up to complex
high-dimensional data.
