  Sparse estimation for Gaussian graphical models is a crucial technique for
making the relationships among numerous observed variables more interpretable
and quantifiable. Various methods have been proposed, including graphical
lasso, which utilizes the $\ell_1$ norm as a regularization term, as well as
methods employing non-convex regularization terms. However, most of these
methods approximate the $\ell_0$ norm with convex functions. To estimate more
accurate solutions, it is desirable to treat the $\ell_0$ norm directly as a
regularization term. In this study, we formulate the sparse estimation problem
for Gaussian graphical models using the $\ell_0$ norm and propose a method to
solve this problem using the Difference of Convex functions Algorithm (DCA).
Specifically, we convert the $\ell_0$ norm constraint into an equivalent
largest-$K$ norm constraint, reformulate the constrained problem into a
penalized form, and solve it using the DC algorithm (DCA). Furthermore, we
designed an algorithm that efficiently computes using graphical lasso.
Experimental results with synthetic data show that our method yields results
that are equivalent to or better than existing methods. Comparisons of model
learning through cross-validation confirm that our method is particularly
advantageous in selecting true edges.
