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The optimization problems with a sparsity constraint is a class of important global optimization problems. A typical type of thresholding algorithms for solving such a problem adopts the traditional full steepest descent direction or…
In statistics, generalized linear models (GLMs) are widely used for modeling data and can expressively capture potential nonlinear dependence of the model's outcomes on its covariates. Within the broad family of GLMs, those with binary…
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…
Probabilistic Graphical Models (PGMs) are generative models of complex systems. They rely on conditional independence assumptions between variables to learn sparse representations which can be visualized in a form of a graph. Such models…
Iterative algorithms based on thresholding, feedback and null space tuning (NST+HT+FB) for sparse signal recovery are exceedingly effective and fast, particularly for large scale problems. The core algorithm is shown to converge in finitely…
An important class of problems involves training deep neural networks with sparse prediction targets of very high dimension D. These occur naturally in e.g. neural language models or the learning of word-embeddings, often posed as…
Sparse approximation is important in many applications because of concise form of an approximant and good accuracy guarantees. The theory of compressed sensing, which proved to be very useful in the image processing and data sciences, is…
In this article a unified approach to iterative soft-thresholding algorithms for the solution of linear operator equations in infinite dimensional Hilbert spaces is presented. We formulate the algorithm in the framework of generalized…
Current orthogonal matching pursuit (OMP) algorithms calculate the correlation between two vectors using the inner product operation and minimize the mean square error, which are both suboptimal when there are non-Gaussian noises or…
The performance of Orthogonal Matching Pursuit (OMP) for variable selection is analyzed for random designs. When contrasted with the deterministic case, since the performance is here measured after averaging over the distribution of the…
The reconstruction of sparse signals requires the solution of an $\ell_0$-norm minimization problem in Compressed Sensing. Previous research has focused on the investigation of a single candidate to identify the support (index of nonzero…
Sorting is a fundamental operation of all computer systems, having been a long-standing significant research topic. Beyond the problem formulation of traditional sorting algorithms, we consider sorting problems for more abstract yet…
Sparse recovery methods are essential for channel estimation and localization in modern communication systems, but their reliability relies on accurate physical models, which are rarely perfectly known. Their computational complexity also…
A dedicated algorithm for sparse spectral representation of music sound is presented. The goal is to enable the representation of a piece of music signal, as a linear superposition of as few spectral components as possible. A representation…
Direction of Arrival (DOA) estimation of multiple narrow-band coherent or partially coherent sources is a major challenge in array signal processing. Though many subspace- based algorithms are available in literature, none of them tackle…
We conducted an extensive computational experiment, lasting multiple CPU-years, to optimally select parameters for two important classes of algorithms for finding sparse solutions of underdetermined systems of linear equations. We make the…
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…
The compression of deep neural networks (DNNs) to reduce inference cost becomes increasingly important to meet realistic deployment requirements of various applications. There have been a significant amount of work regarding network…
Greed is good. However, the tighter you squeeze, the less you have. In this paper, a less greedy algorithm for sparse signal reconstruction in compressive sensing, named orthogonal matching pursuit with thresholding is studied. Using the…
For compressed sensing over arbitrarily connected networks, we consider the problem of estimating underlying sparse signals in a distributed manner. We introduce a new signal model that helps to describe inter-signal correlation among…