Related papers: On block coherence of frames
In high-stakes engineering applications, optimization algorithms must come with provable worst-case guarantees over a mathematically defined class of problems. Designing for the worst case, however, inevitably sacrifices performance on the…
We prove upper bounds on the order of convergence of lattice based algorithms for numerical integration in function spaces of dominating mixed smoothness on the unit cube with homogeneous boundary condition. More precisely, we study…
In many practical applications including remote sensing, multi-task learning, and multi-spectrum imaging, data are described as a set of matrices sharing a common column space. We consider the joint estimation of such matrices from their…
Construction on the measurement matrix $A$ is a central problem in compressed sensing. Although using random matrices is proven optimal and successful in both theory and applications. A deterministic construction on the measurement matrix…
Model compression is generally performed by using quantization, low-rank approximation or pruning, for which various algorithms have been researched in recent years. One fundamental question is: what types of compression work better for a…
Errors occurring on noisy hardware pose a key challenge to reliable quantum computing. Existing techniques such as error correction, mitigation, or suppression typically separate the error handling from the algorithm analysis and design. In…
This paper considers the problem of recovery of a low-rank matrix in the situation when most of its entries are not observed and a fraction of observed entries are corrupted. The observations are noisy realizations of the sum of a low rank…
This paper first proposes an N-block PCPM algorithm to solve N-block convex optimization problems with both linear and nonlinear constraints, with global convergence established. A linear convergence rate under the strong second-order…
This paper studies computationally efficient methods and their minimax optimality for high-dimensional clustering and signal recovery under block signal structures. We propose two sets of methods, cross-block feature aggregation PCA…
The problem of finding a $k \times k$ submatrix of maximum volume of a matrix $A$ is of interest in a variety of applications. For example, it yields a quasi-best low-rank approximation constructed from the rows and columns of $A$. We show…
For experiments running in field plots or over time, the observations are often correlated due to spatial or serial correlation, which leads to correlated errors in a linear model analyzing the treatment means. Without knowing the exact…
We introduce a general framework to deterministically construct binary measurement matrices for compressed sensing. The proposed matrices are composed of (circulant) permutation submatrix blocks and zero submatrix blocks, thus making their…
We study the problem of community recovery and detection in multi-layer stochastic block models, focusing on the critical network density threshold for consistent community structure inference. Using a prototypical two-block model, we…
We propose a unified framework to solve general low-rank plus sparse matrix recovery problems based on matrix factorization, which covers a broad family of objective functions satisfying the restricted strong convexity and smoothness…
We consider the problems of detection and localization of a contiguous block of weak activation in a large matrix, from a small number of noisy, possibly adaptive, compressive (linear) measurements. This is closely related to the problem of…
We provide a computational framework for approximating a class of structured matrices; here, the term structure is very general, and may refer to a regular sparsity pattern (e.g., block-banded), or be more highly structured (e.g., symmetric…
Block-sparse regularization is already well-known in active thermal imaging and is used for multiple measurement based inverse problems. The main bottleneck of this method is the choice of regularization parameters which differs for each…
In distributed optimization, the communication of model updates can be a performance bottleneck. Consequently, gradient compression has been proposed as a means of increasing optimization throughput. In general, due to information loss,…
This paper deals with the problem of robust matrix completion -- retrieving a low-rank matrix and a sparse matrix from the compressed counterpart of their superposition. Though seemingly not an unresolved issue, we point out that the…
Quantum coherence, as a direct manifestation of the quantum superposition principle, is a crucial resource in quantum information processing. Block coherence resource theory generalizes the traditional coherence framework by defining…