arXiv subjects

Yanyun Ding

Publications and source records attributed to Yanyun Ding.

6 recordsLinked to original sources

arXiv2026

ADMM-based Bilevel Descent Aggregation Algorithm for Sparse Hyperparameter Selection

It is widely acknowledged that hyperparameter selection plays a critical role in the effectiveness of sparse optimization problems. The bilevel optimization provides a robust framework for addressing this issue, but these existing methods depend heavily on the lower-level singleton (LLS) assumption, which greatly limits their practical applicabilities. To tackle this technical challenge, this paper focus on a particular type of nonsmooth convex sparse optimization problem and presents a new bilevel optimization framework. This framework effectively integrates the alternating direction method of multipliers (ADMM) with a bilevel descent aggregation (BDA) algorithm. Specifically, it employs ADMM to efficiently address the lower-level problem and uses BDA to explore the hyperparameter space, thereby integrating both the upper and lower-level problems. It is important to emphasize that a key contribution of this paper lies in the presentation of a novel convergence analysis. The analysis illustrates that the proposed ADMM-BDA algorithm achieves global convergence under significantly relaxed conditions, thereby departing from the LLS assumption that are often required in the literature. We conduct a series of numerical experiments utilizing synthetic and real-world data, and do performance comparisions against some state-of-the-art algorithms. The results indicates that ADMM-BDA exhibits superior effectiveness and robustness for solving bilevel programming problems, especially when the lower-level problem is an elastic-net penalized statistics problem.

math.OC↗

arXiv2025

A Primal Dual Active Set with Continuation Algorithm for $\ell_0$-Penalized High-dimensional Accelerated Failure Time Model

The accelerated failure time model has garnered attention due to its intuitive linear regression interpretation and has been successfully applied in fields such as biostatistics, clinical medicine, economics, and social sciences. This paper considers a weighted least squares estimation method with an $\ell_0$-penalty based on right-censored data in a high-dimensional setting. For practical implementation, we adopt an efficient primal dual active set algorithm and utilize a continuous strategy to select the appropriate regularization parameter. By employing the mutual incoherence property and restricted isometry property of the covariate matrix, we perform an error analysis for the estimated variables in the active set during the iteration process. Furthermore, we identify a distinctive monotonicity in the active set and show that the algorithm terminates at the oracle solution in a finite number of steps. Finally, we perform extensive numerical experiments using both simulated data and real breast cancer datasets to assess the performance benefits of our method in comparison to other existing approaches.

stat.ME↗

arXiv2024

Iterative Reweighted Framework Based Algorithms for Sparse Linear Regression with Generalized Elastic Net Penalty

The elastic net penalty is frequently employed in high-dimensional statistics for parameter regression and variable selection. It is particularly beneficial compared to lasso when the number of predictors greatly surpasses the number of observations. However, empirical evidence has shown that the $\ell_q$-norm penalty (where $0 < q < 1$) often provides better regression compared to the $\ell_1$-norm penalty, demonstrating enhanced robustness in various scenarios. In this paper, we explore a generalized elastic net model that employs a $\ell_r$-norm (where $r \geq 1$) in loss function to accommodate various types of noise, and employs a $\ell_q$-norm (where $0 < q < 1$) to replace the $\ell_1$-norm in elastic net penalty. Theoretically, we establish the computable lower bounds for the nonzero entries of the generalized first-order stationary points of the proposed generalized elastic net model. For implementation, we develop two efficient algorithms based on the locally Lipschitz continuous $ε$-approximation to $\ell_q$-norm. The first algorithm employs an alternating direction method of multipliers (ADMM), while the second utilizes a proximal majorization-minimization method (PMM), where the subproblems are addressed using the semismooth Newton method (SNN). We also perform extensive numerical experiments with both simulated and real data, showing that both algorithms demonstrate superior performance. Notably, the PMM-SSN is efficient than ADMM, even though the latter provides a simpler implementation.

stat.ML↗

arXiv2021

An Efficient Semismooth Newton Method for Adaptive Sparse Signal Recovery Problems

We know that compressive sensing can establish stable sparse recovery results from highly undersampled data under a restricted isometry property condition. In reality, however, numerous problems are coherent, and vast majority conventional methods might work not so well. Recently, it was shown that using the difference between $\ell_1$- and $\ell_2$-norm as a regularization always has superior performance. In this paper, we propose an adaptive $\ell_p$-$\ell_{1-2}$ model where the $\ell_p$-norm with $p\geq 1$ measures the data fidelity and the $\ell_{1-2}$-term measures the sparsity. This proposed model has the ability to deal with different types of noises and extract the sparse property even under high coherent condition. We use a proximal majorization-minimization technique to handle the nonconvex regularization term and then employ a semismooth Newton method to solve the corresponding convex relaxation subproblem. We prove that the sequence generated by the semismooth Newton method admits fast local convergence rate to the subproblem under some technical assumptions. Finally, we do some numerical experiments to demonstrate the superiority of the proposed model and the progressiveness of the proposed algorithm.

math.OC↗

arXiv2021

Efficient Dual ADMMs for Sparse Compressive Sensing MRI Reconstruction

Magnetic Resonance Imaging (MRI) is a kind of medical imaging technology used for diagnostic imaging of diseases, but its image quality may be suffered by the long acquisition time. The compressive sensing (CS) based strategy may decrease the reconstruction time greatly, but it needs efficient reconstruction algorithms to produce high-quality and reliable images. This paper focuses on the algorithmic improvement for the sparse reconstruction of CS-MRI, especially considering a non-smooth convex minimization problem which is composed of the sum of a total variation regularization term and a $\ell_1$-norm term of the wavelet transformation. The partly motivation of targeting the dual problem is that the dual variables are involved in relatively low-dimensional subspace. Instead of solving the primal model as usual, we turn our attention to its associated dual model composed of three variable blocks and two separable non-smooth function blocks. However, the directly extended alternating direction method of multipliers (ADMM) must be avoided because it may be divergent, although it usually performs well numerically. In order to solve the problem, we employ a symmetric Gauss-Seidel (sGS) technique based ADMM. Compared with the directly extended ADMM, this method only needs one additional iteration, but its convergence can be guaranteed theoretically. Besides, we also propose a generalized variant of ADMM because this method has been illustrated to be efficient for solving semidefinite programming in the past few years. Finally, we do extensive experiments on MRI reconstruction using some simulated and real MRI images under different sampling patterns and ratios. The numerical results demonstrate that the proposed algorithms significantly achieve high reconstruction accuracies with fast computational speed.

math.OC↗

arXiv2018

Symmetric Gauss-Seidel Technique Based Alternating Direction Methods of Multipliers for Transform Invariant Low-Rank Textures Problem

Transform Invariant Low-Rank Textures, referred to as TILT, can accurately and robustly extract textural or geometric information in a 3D from user-specified windows in 2D in spite of significant corruptions and warping. It was discovered that the task can be characterized, both theoretically and numerically, by solving a sequence of matrix nuclear-norm and $\ell_1$-norm involved convex minimization problems. For solving this problem, the direct extension of Alternating Direction Method of Multipliers (ADMM) in an usual Gauss-Seidel manner often performs numerically well in practice but there is no theoretical guarantee on its convergence. In this paper, we resolve this dilemma by using the novel symmetric Gauss-Seidel (sGS) based ADMM developed by Li, Sun \& Toh (Math. Prog. 2016). The sGS-ADMM is guaranteed to converge and we shall demonstrate in this paper that it is also practically efficient than the directly extended ADMM. When the sGS technique is applied to this particular problem, we show that only one variable needs to be re-updated, and this updating hardly imposes any excessive computational cost. The sGS decomposition theorem of Li, Sun \& Toh (arXiv: 1703.06629) establishes the equivalent between sGS-ADMM and the classical ADMM with an additional semi-proximal term, so the convergence result is followed directly. Extensive experiments illustrate that the sGS-ADMM and its generalized variant have superior numerical efficiency over the directly extended ADMM.

math.OC↗