Review for NeurIPS paper: Nonconvex Sparse Graph Learning under Laplacian Constrained Graphical Model

Weaknesses: Theorem 3.1 and its empirical results in Figure 1 bring the following concern: The fully connected graph obtained by lambda larger than certain value (e.g., lambda*), which is related to the input data covariance S. So, the scaling of X impacts lambda*. How does the lambda from 0 to lambda* theoretically impact the sparsity of the optimal graph? The proposed algorithm for solving nonconvex optimization is the combination of linearization of nonconvex regularization and projected gradient descent method. The convergence results are shown in Theorem 3.8. This can guarantee the convergence, but how many iterations are required for both inner and outer iterations in Algorithm 1 and what is the computational complexity?