Related papers: Solutions to Multilevel Sparse Matrix Problems
Multilevel models (mixed-effect models or hierarchical linear models) are now a standard approach to analysing clustered and longitudinal data in the social, behavioural and medical sciences. This review article focuses on multilevel linear…
Coded recurrent neural networks with three levels of sparsity are introduced. The first level is related to the size of messages, much smaller than the number of available neurons. The second one is provided by a particular coding rule,…
With the advent of massive data sets much of the computational science and engineering community has moved toward data-intensive approaches in regression and classification. However, these present significant challenges due to increasing…
Network alignment generalizes and unifies several approaches for forming a matching or alignment between the vertices of two graphs. We study a mathematical programming framework for network alignment problem and a sparse variation of it…
The most common procedure to solve a linear bilevel problem in the PES community is, by far, to transform it into an equivalent single-level problem by replacing the lower level with its KKT optimality conditions. Then, the complementarity…
Sparse representations using data dictionaries provide an efficient model particularly for signals that do not enjoy alternate analytic sparsifying transformations. However, solving inverse problems with sparsifying dictionaries can be…
Iterative methods based on matrix splittings are useful in solving large sparse linear systems. In this direction, proper splittings and its several extensions are used to deal with singular and rectangular linear systems. In this article,…
Repeated measurements are common in many fields, where random variables are observed repeatedly across different subjects. Such data have an underlying hierarchical structure, and it is of interest to learn covariance/correlation at…
The increasing availability of massive data sets poses a series of challenges for machine learning. Prominent among these is the need to learn models under hardware or human resource constraints. In such resource-constrained settings, a…
Sparse principal component analysis addresses the problem of finding a linear combination of the variables in a given data set with a sparse coefficients vector that maximizes the variability of the data. This model enhances the ability to…
This paper addresses the problem of fault diagnosis in multistation assembly systems. Fault diagnosis is to identify process faults that cause the excessive dimensional variation of the product using dimensional measurements. For such…
Machine learning has been successfully applied to various fields of scientific computing in recent years. In this work, we propose a sparse radial basis function neural network method to solve elliptic partial differential equations (PDEs)…
Solving linear systems is often the computational bottleneck in real-life problems. Iterative solvers are the only option due to the complexity of direct algorithms or because the system matrix is not explicitly known. Here, we develop a…
Sparse linear (or generalized linear) models combine a standard likelihood function with a sparse prior on the unknown coefficients. These priors can conveniently be expressed as a maximization over zero-mean Gaussians with different…
We consider the problem of robust matrix completion, which aims to recover a low rank matrix $L_*$ and a sparse matrix $S_*$ from incomplete observations of their sum $M=L_*+S_*\in\mathbb{R}^{m\times n}$. Algorithmically, the robust matrix…
Multilevel or hierarchical data structures can occur in many areas of research, including economics, psychology, sociology, agriculture, medicine, and public health. Over the last 25 years, there has been increasing interest in developing…
We propose a novel approach to the problem of multilevel clustering, which aims to simultaneously partition data in each group and discover grouping patterns among groups in a potentially large hierarchically structured corpus of data. Our…
We consider the problem of sparse matrix multiplication by the column row method in a distributed setting where the matrix product is not necessarily sparse. We present a surprisingly simple method for "consistent" parallel processing of…
Matrix recovery from sparse observations is an extensively studied topic emerging in various applications, such as recommendation system and signal processing, which includes the matrix completion and compressed sensing models as special…
We present a new hybrid direct/iterative approach to the solution of a special class of saddle point matrices arising from the discretization of the steady incompressible Navier-Stokes equations on an Arakawa C-grid. The two-level method…