Related papers: Krylov Methods for Low-Rank Regularization
The problem of joint feature selection across a group of related tasks has applications in many areas including biomedical informatics and computer vision. We consider the l2,1-norm regularized regression model for joint feature selection…
Low-rank learning has attracted much attention recently due to its efficacy in a rich variety of real-world tasks, e.g., subspace segmentation and image categorization. Most low-rank methods are incapable of capturing low-dimensional…
This paper develops a new class of Rosenbrock-type integrators based on a Krylov space solution of the linear systems. The new family, called Rosenbrock-Krylov (Rosenbrock-K), is well suited for solving large scale systems of ODEs or…
Low-rank modeling has a lot of important applications in machine learning, computer vision and social network analysis. While the matrix rank is often approximated by the convex nuclear norm, the use of nonconvex low-rank regularizers has…
Tikhonov regularization is a common technique used when solving poorly behaved optimization problems. Often, and with good reason, this technique is applied by practitioners in an ad hoc fashion. In this note, we systematically illustrate…
Block Krylov subspace methods (KSMs) comprise building blocks in many state-of-the-art solvers for large-scale matrix equations as they arise, e.g., from the discretization of partial differential equations. While extended and rational…
One of the most computationally expensive steps of the low-rank ADI method for large-scale Lyapunov equations is the solution of a shifted linear system at each iteration. We propose the use of the extended Krylov subspace method for this…
The iterated Arnoldi-Tikhonov (iAT) method is a regularization technique particularly suited for solving large-scale ill-posed linear inverse problems. Indeed, it reduces the computational complexity through the projection of the…
There has been tremendous research on the design of image regularizers over the years, from simple Tikhonov and Laplacian to sophisticated sparsity and CNN-based regularizers. Coupled with a model-based loss function, these are typically…
We design a new iterative algorithm, called REINFORCE-OPT, for solving a general type of optimization problems. This algorithm parameterizes the solution search rule and iteratively updates the parameter using a reinforcement learning (RL)…
In this paper, we investigate the use of multilinear algebra for reducing the order of multidimensional linear time-invariant (MLTI) systems. Our main tools are tensor rational Krylov subspace methods, which enable us to approximate the…
The least-square regression problems or inverse problems have been widely studied in many fields such as compressive sensing, signal processing, and image processing. To solve this kind of ill-posed problems, a regularization term (i.e.,…
Iterative regularization exploits the implicit bias of an optimization algorithm to regularize ill-posed problems. Constructing algorithms with such built-in regularization mechanisms is a classic challenge in inverse problems but also in…
This paper, broadly speaking, covers the use of randomness in two main areas: low-rank approximation and kernel methods. Low-rank approximation is very important in numerical linear algebra. Many applications depend on matrix decomposition…
For the large-scale linear discrete ill-posed problem $\min\|Ax-b\|$ or $Ax=b$ with $b$ contaminated by Gaussian white noise, there are four commonly used Krylov solvers: LSQR and its mathematically equivalent CGLS, the Conjugate Gradient…
Several problems in machine learning, statistics, and other fields rely on computing eigenvectors. For large scale problems, the computation of these eigenvectors is typically performed via iterative schemes such as subspace iteration or…
For the large-scale linear discrete ill-posed problem $\min\|Ax-b\|$ or $Ax=b$ with $b$ contaminated by a white noise, the Lanczos bidiagonalization based LSQR method and its mathematically equivalent Conjugate Gradient (CG) method for…
The paper addresses the problem of low-rank trace norm minimization. We propose an algorithm that alternates between fixed-rank optimization and rank-one updates. The fixed-rank optimization is characterized by an efficient factorization…
Rational Krylov subspaces have become a reference tool in dimension reduction procedures for several application problems. When data matrices are symmetric, a short-term recurrence can be used to generate an associated orthonormal basis. In…
The numerical solution of linear discrete ill-posed problems typically requires regularization, i.e., replacement of the available ill-conditioned problem by a nearby better conditioned one. The most popular regularization methods for…