Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userA Homotopy Coordinate Descent Optimization Method for $l_0$-Norm Regularized Least Square Problem
107
0
0.0
(
0
)
Added by
Zhenzhen Sun
Publication date
2020
fields
Informatics Engineering
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
This paper proposes a homotopy coordinate descent (HCD) method to solve the $l_0$-norm regularized least square ($l_0$-LS) problem for compressed sensing, which combine the homotopy technique with a variant of coordinate descent method. Differs from the classical coordinate descent algorithms, HCD provides three strategies to speed up the convergence: warm start initialization, active set updating, and strong rule for active set initialization. The active set is pre-selected using a strong rule, then the coordinates of the active set are updated while those of inactive set are unchanged. The homotopy strategy provides a set of warm start initial solutions for a sequence of decreasing values of the regularization factor, which ensures all iterations along the homotopy solution path are sparse. Computational experiments on simulate signals and natural signals demonstrate effectiveness of the proposed algorithm, in accurately and efficiently reconstructing sparse solutions of the $l_0$-LS problem, whether the observation is noisy or not.
rate research
Read More
We propose Shotgun, a parallel coordinate descent algorithm for minimizing L1-regularized losses. Though coordinate descent seems inherently sequential, we prove convergence bounds for Shotgun which predict linear speedups, up to a problem-dependent limit. We present a comprehensive empirical study of Shotgun for Lasso and sparse logistic regression. Our theoretical predictions on the potential for parallelism closely match behavior on real data. Shotgun outperforms other published solvers on a range of large problems, proving to be one of the most scalable algorithms for L1.
This paper is concerned with a class of zero-norm regularized piecewise linear-quadratic (PLQ) composite minimization problems, which covers the zero-norm regularized $ell_1$-loss minimization problem as a special case. For this class of nonconvex nonsmooth problems, we show that its equivalent MPEC reformulation is partially calm on the set of global optima and make use of this property to derive a family of equivalent DC surrogates. Then, we propose a proximal majorization-minimization (MM) method, a convex relaxation approach not in the DC algorithm framework, for solving one of the DC surrogates which is a semiconvex PLQ minimization problem involving three nonsmooth terms. For this method, we establish its global convergence and linear rate of convergence, and under suitable conditions show that the limit of the generated sequence is not only a local optimum but also a good critical point in a statistical sense. Numerical experiments are conducted with synthetic and real data for the proximal MM method with the subproblems solved by a dual semismooth Newton method to confirm our theoretical findings, and numerical comparisons with a convergent indefinite-proximal ADMM for the partially smoothed DC surrogate verify its superiority in the quality of solutions and computing time.
We present a novel randomized block coordinate descent method for the minimization of a convex composite objective function. The method uses (approximate) partial second-order (curvature) information, so that the algorithm performance is more robust when applied to highly nonseparable or ill conditioned problems. We call the method Flexible Coordinate Descent (FCD). At each iteration of FCD, a block of coordinates is sampled randomly, a quadratic model is formed about that block and the model is minimized emph{approximately/inexactly} to determine the search direction. An inexpensive line search is then employed to ensure a monotonic decrease in the objective function and acceptance of large step sizes. We present several high probability iteration complexity results to show that convergence of FCD is guaranteed theoretically. Finally, we present numerical results on large-scale problems to demonstrate the practical performance of the method.
We propose and study a regularization method for recovering an approximate electrical conductivity solely from the magnitude of one interior current density field. Without some minimal knowledge of the boundary voltage potential, the problem has been recently shown to have nonunique solutions, thus recovering the exact conductivity is impossible. The method is based on solving a weighted least gradient problem in the subspace of functions of bounded variations with square integrable traces. The computational effectiveness of this method is demonstrated in numerical experiments.
The simplicity of gradient descent (GD) made it the default method for training ever-deeper and complex neural networks. Both loss functions and architectures are often explicitly tuned to be amenable to this basic local optimization. In the context of weakly-supervised CNN segmentation, we demonstrate a well-motivated loss function where an alternative optimizer (ADM) achieves the state-of-the-art while GD performs poorly. Interestingly, GD obtains its best result for a smoother tuning of the loss function. The results are consistent across different network architectures. Our loss is motivated by well-understood MRF/CRF regularization models in shallow segmentation and their known global solvers. Our work suggests that network design/training should pay more attention to optimization methods.
suggested questions
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
