Papers › DC Algorithm for Estimation of Sparse Gaussian Graphical Models
DC Algorithm for Estimation of Sparse Gaussian Graphical Models
Tomokaze Shiratori, Yuichi Takano
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 ℓ₁ norm as a regularization term, as well as methods employing non-convex regularization terms. However, most of these methods approximate the ℓ₀ norm with convex functions. To estimate more accurate solutions, it is desirable to treat the ℓ₀ norm directly as a regularization term. In this study, we formulate the sparse estimation problem for Gaussian graphical models using the ℓ₀ norm and propose a method to solve this problem using the Difference of Convex functions Algorithm (DCA). Specifically, we convert the ℓ₀ 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.
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