Related papers: Sparse approximation by greedy algorithms
We connect high-dimensional subset selection and submodular maximization. Our results extend the work of Das and Kempe (2011) from the setting of linear regression to arbitrary objective functions. For greedy feature selection, this…
Compressed sensing (CS) is a sampling theory that allows reconstruction of sparse (or compressible) signals from an incomplete number of measurements, using of a sensing mechanism implemented by an appropriate projection matrix. The CS…
Sequential Compressive Sensing, which may be widely used in sensing devices, is a popular topic of recent research. This paper proposes an online recovery algorithm for sparse approximation of sequential compressive sensing. Several…
The celebrated sparse representation model has led to remarkable results in various signal processing tasks in the last decade. However, despite its initial purpose of serving as a global prior for entire signals, it has been commonly used…
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…
We introduce a new interpretation of sparse variational approximations for Gaussian processes using inducing points, which can lead to more scalable algorithms than previous methods. It is based on decomposing a Gaussian process as a sum of…
Low-rank model order reduction strategies for contact mechanics show limited dimensionality reduction due to linear inseparability of contact pressure field. Therefore, a dictionary based strategy is explored for creating efficient models…
This paper treats the problem of minimizing a general continuously differentiable function subject to sparsity constraints. We present and analyze several different optimality criteria which are based on the notions of stationarity and…
Applying the theory of compressive sensing in practice always takes different kinds of perturbations into consideration. In this paper, the recovery performance of greedy pursuits with replacement for sparse recovery is analyzed when both…
Local-search methods are widely employed in statistical applications, yet interestingly, their theoretical foundations remain rather underexplored, compared to other classes of estimators such as low-degree polynomials and spectral methods.…
Sparse representation using over-complete dictionaries have shown to produce good quality results in various image processing tasks. Dictionary learning algorithms have made it possible to engineer data adaptive dictionaries which have…
We study here sparse recovery problems in the presence of additive noise. We analyze a thresholding version of the CoSaMP algorithm, named Thresholding Greedy Pursuit (TGP). We demonstrate that an appropriate choice of thresholding…
Performing signal processing tasks on compressive measurements of data has received great attention in recent years. In this paper, we extend previous work on compressive dictionary learning by showing that more general random projections…
We consider the sparse contextual bandit problem where arm feature affects reward through the inner product of sparse parameters. Recent studies have developed sparsity-agnostic algorithms based on the greedy arm selection policy. However,…
The SparseStep algorithm is presented for the estimation of a sparse parameter vector in the linear regression problem. The algorithm works by adding an approximation of the exact counting norm as a constraint on the model parameters and…
Graph-based approaches are empirically shown to be very successful for the nearest neighbor search (NNS). However, there has been very little research on their theoretical guarantees. We fill this gap and rigorously analyze the performance…
We present new convergence estimates of generalized empirical interpolation methods in terms of the entropy numbers of the parametrized function class. Our analysis is transparent and leads to sharper convergence rates than the classical…
Sparse regression and classification estimators that respect group structures have application to an assortment of statistical and machine learning problems, from multitask learning to sparse additive modeling to hierarchical selection.…
This paper describes a simple greedy D-approximation algorithm for any covering problem whose objective function is submodular and non-decreasing, and whose feasible region can be expressed as the intersection of arbitrary (closed upwards)…
We propose a novel sparse preference learning/ranking algorithm. Our algorithm approximates the true utility function by a weighted sum of basis functions using the squared loss on pairs of data points, and is a generalization of the kernel…