  A common challenge in estimating parameters of probability density functions
is the intractability of the normalizing constant. While in such cases maximum
likelihood estimation may be implemented using numerical integration, the
approach becomes computationally intensive. In contrast, the score matching
method of Hyv\"arinen (2005) avoids direct calculation of the normalizing
constant and yields closed-form estimates for exponential families of
continuous distributions over $\mathbb{R}^m$. Hyv\"arinen (2007) extended the
approach to distributions supported on the non-negative orthant
$\mathbb{R}_+^m$. In this paper, we give a generalized form of score matching
for non-negative data that improves estimation efficiency. We also generalize
the regularized score matching method of Lin et al. (2016) for non-negative
Gaussian graphical models, with improved theoretical guarantees.
