Related papers: On the Optimality of Backward Regression: Sparse R…
The sparse matrix compression problem asks for a one-dimensional representation of a binary $n \times \ell$ matrix, formed by an integer array of row indices and a shift function for each row, such that accessing a matrix entry is possible…
Sparse residual tree (SRT) is an adaptive exploration method for multivariate scattered data approximation. It leads to sparse and stable approximations in areas where the data is sufficient or redundant, and points out the possible local…
Cooperative Greedy Pursuit Strategies are considered for approximating a signal partition subjected to a global constraint on sparsity. The approach aims at producing a high quality sparse approximation of the whole signal, using highly…
Sensor selection refers to the problem of intelligently selecting a small subset of a collection of available sensors to reduce the sensing cost while preserving signal acquisition performance. The majority of sensor selection algorithms…
Precision matrix estimation is an important problem in statistical data analysis. This paper introduces a fast sparse precision matrix estimation algorithm, namely GISS$^{{\rho}}$, which is originally introduced for compressive sensing. The…
In this paper, we revisit the large-scale constrained linear regression problem and propose faster methods based on some recent developments in sketching and optimization. Our algorithms combine (accelerated) mini-batch SGD with a new…
Best subset selection is considered the `gold standard' for many sparse learning problems. A variety of optimization techniques have been proposed to attack this non-convex and NP-hard problem. In this paper, we investigate the dual forms…
The shuffled linear regression problem aims to recover linear relationships in datasets where the correspondence between input and output is unknown. This problem arises in a wide range of applications including survey data, in which one…
This paper proposes a sparse regression method that continuously interpolates between Forward Stepwise selection (FS) and the LASSO. When tuned appropriately, our solutions are much sparser than typical LASSO fits but, unlike FS fits,…
It is well known that $\ell_1$ minimization can be used to recover sufficiently sparse unknown signals from compressed linear measurements. In fact, exact thresholds on the sparsity, as a function of the ratio between the system dimensions,…
Text retrieval using learned sparse representations of queries and documents has, over the years, evolved into a highly effective approach to search. It is thanks to recent advances in approximate nearest neighbor search-with the emergence…
Results on two different settings of asymptotic behavior of approximation characteristics of individual functions are presented. First, we discuss the following classical question for sparse approximation. Is it true that for any individual…
In many practical applications such as direction-of-arrival (DOA) estimation and line spectral estimation, the sparsifying dictionary is usually characterized by a set of unknown parameters in a continuous domain. To apply the conventional…
Backtracking is a basic strategy to solve constraint satisfaction problems (CSPs). A satisfiable CSP instance is backtrack-free if a solution can be found without encountering any dead-end during a backtracking search, implying that the…
We discuss a method for sparse signal approximation, which is based on the correlation of the target signal with a pseudo-random signal, and uses a modification of the greedy matching pursuit algorithm. We show that this approach provides…
We demonstrate a simple greedy algorithm that can reliably recover a d-dimensional vector v from incomplete and inaccurate measurements x. Here our measurement matrix is an N by d matrix with N much smaller than d. Our algorithm,…
Sparse training is a natural idea to accelerate the training speed of deep neural networks and save the memory usage, especially since large modern neural networks are significantly over-parameterized. However, most of the existing methods…
Space-time adaptive processing (STAP) algorithms with coprime arrays can provide good clutter suppression potential with low cost in airborne radar systems as compared with their uniform linear arrays counterparts. However, the performance…
Large-scale non-convex sparsity-constrained problems have recently gained extensive attention. Most existing deterministic optimization methods (e.g., GraSP) are not suitable for large-scale and high-dimensional problems, and thus…
Huge scale machine learning problems are nowadays tackled by distributed optimization algorithms, i.e. algorithms that leverage the compute power of many devices for training. The communication overhead is a key bottleneck that hinders…