Title: Efficient coordinate descent algorithm for sparse precision matrix estimation via scaled Lasso
Authors: Donghyeon Yu - Inha University (Korea, South) [presenting]
Abstract: Sparse precision matrix plays an important role in Gaussian graphical model due to the fact that a zero off-diagonal element denotes the conditional independence of two corresponding variables given others. In the Gaussian graphical model, lots of methods have been developed and their theoretical properties are given as well. Among them, the sparse precision matrix estimation via scaled lasso (SPMESL) has an attractive feature that automatically sets the penalty level to achieve the optimal convergence rate under the sparsity and the invertibility conditions, while other methods have to search for optimal tuning parameters. Yet, despite its advantage, the SPMESL is not widely used due to its expensive computational cost and the restricted assumptions. The coordinate descent (CD) algorithm for the SPMESL is considered, and it is shown to be numerically more efficient than the least angle regression (LARS). In addition, we develop a parallel CD algorithm using graphics processing units for scalability. Numerical study is also conducted to investigate the sensitivity of the SPMESL to the theoretical assumptions, and shows that the SPMESL has the smallest false discovery rate for all cases and the best performance in cases where the level of sparsity of columns is high.