Related papers: On Structural Rank and Resilience of Sparsity Patt…
We define and solve classes of sparse matrix problems that arise in multilevel modeling and data analysis. The classes are indexed by the number of nested units, with two-level problems corresponding to the common situation in which data on…
The topic of recovery of a structured model given a small number of linear observations has been well-studied in recent years. Examples include recovering sparse or group-sparse vectors, low-rank matrices, and the sum of sparse and low-rank…
We consider the problem of computing the rank of an m x n matrix A over a field. We present a randomized algorithm to find a set of r = rank(A) linearly independent columns in \~O(|A| + r^\omega) field operations, where |A| denotes the…
Although sparse neural networks have been studied extensively, the focus has been primarily on accuracy. In this work, we focus instead on network structure, and analyze three popular algorithms. We first measure performance when structure…
Matrix completion is a classical problem that has received recurring interest across a wide range of fields. In this paper, we revisit this problem in an ultra-sparse sampling regime, where each entry of an unknown, $n\times d$ matrix $M$…
A matrix space of size $m\times n$ is a linear subspace of the linear space of $m\times n$ matrices over a field $\mathbb{F}$. The rank of a matrix space is defined as the maximal rank over matrices in this space. A matrix space…
This paper addresses spatial programming of sparse matrix computations for productive performance. The challenge is how to express an irregular computation and its optimizations in a regular way. A sparse matrix has (non-zero) values and a…
We consider the linear complementarity problem with uncertain data modeled by intervals, representing the range of possible values. Many properties of the linear complementarity problem (such as solvability, uniqueness, convexity, finite…
Hierarchical structure and repetition are prevalent in graphs originating from nature or engineering. These patterns can be represented by a class of parametric-structure graphs, which are defined by templates that generate structure by way…
We propose a probe for the analysis of deep learning architectures that is based on machine learning and approximation theoretical principles. Given a deep learning architecture and a training set, during or after training, the Sparsity…
Matrix Completion is the problem of recovering an unknown real-valued low-rank matrix from a subsample of its entries. Important recent results show that the problem can be solved efficiently under the assumption that the unknown matrix is…
Matrix completion constantly receives tremendous attention from many research fields. It is commonly applied for recommender systems such as movie ratings, computer vision such as image reconstruction or completion, multi-task learning such…
This paper considers the matrix completion problem. We show that it is not necessary to assume joint incoherence, which is a standard but unintuitive and restrictive condition that is imposed by previous studies. This leads to a sample…
We consider the problem of determining rank loss conditions for a concatenation of full-rank matrices, such that each row of the composing matrices is scaled by a random coefficient. This problem has applications in wireless interference…
We consider a problem of considerable practical interest: the recovery of a data matrix from a sampling of its entries. Suppose that we observe m entries selected uniformly at random from a matrix M. Can we complete the matrix and recover…
Matrix completion is a modern missing data problem where both the missing structure and the underlying parameter are high dimensional. Although missing structure is a key component to any missing data problems, existing matrix completion…
Given a state transition matrix (STM), we reinvestigate the problem of constructing the sparest input matrix with a fixed number of inputs to guarantee controllability. We give a new and simple graph theoretic characterization for the…
The formation trajectory planning using complete graphs to model collaborative constraints becomes computationally intractable as the number of drones increases due to the curse of dimensionality. To tackle this issue, this paper presents a…
Networks with nodes embedded in a metric space have gained increasing interest in recent years. The effects of spatial embedding on the networks' structural characteristics, however, are rarely taken into account when studying their…
Leveraging on the underlying low-dimensional structure of data, low-rank and sparse modeling approaches have achieved great success in a wide range of applications. However, in many applications the data can display structures beyond simply…