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There has been significant interest in sparse inverse covariance estimation in areas such as statistics, machine learning, and signal processing. In this problem, the sparse inverse of a covariance matrix of a multivariate normal distribution is estimated. A Penalised Log-Likelihood (PLL) optimisation problem is solved to obtain the matrix estimator, where the penalty is responsible for inducing sparsity...
Significant attention has been given to minimizing a penalized least squares criterion for estimating sparse solutions to large linear systems of equations. The penalty induces sparsity and the natural choice is the so-called l0 norm. In this paper we develop a Momentumized Iterative Shrinkage Thresholding (MIST) algorithm for minimizing the resulting non-convex criterion and prove its convergence...
Recently, major attention has been given to penalized log-likelihood estimators for sparse precision (inverse covariance) matrices. The penalty is responsible for inducing sparsity, and a very common choice is the convex l1 norm. However, it is not always the case that the best estimator is achieved with this penalty. So, to improve sparsity and reduce biases associated with the l1 norm, one must...
Recently, there has been a lot of focus on penalized least squares problems for noisy sparse signal estimation. The penalty induces sparsity and a very common choice has been the convex norm. However, to improve sparsity and reduce the biases associated with the norm, one must move to non-convex penalties such as the norm . In this paper we present a novel cyclic descent...
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