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Adapting to a priori unknown noise level is a very important but challenging problem in sequential decision-making as efficient exploration typically requires knowledge of the noise level, which is often loosely specified. We report…
This paper proposes a unified sparsity-aware robust recursive least-squares RLS (S-RRLS) algorithm for the identification of sparse systems under impulsive noise. The proposed algorithm generalizes multiple algorithms only by replacing the…
Learning a generative model of visual information with sparse and compositional features has been a challenge for both theoretical neuroscience and machine learning communities. Sparse coding models have achieved great success in explaining…
Sparse recovery is widely applied in many fields, since many signals or vectors can be sparsely represented under some frames or dictionaries. Most of fast algorithms at present are based on solving $l^0$ or $l^1$ minimization problems and…
For high-dimensional sparse parameter estimation problems, Log-Sum Penalty (LSP) regularization effectively reduces the sampling sizes in practice. However, it still lacks theoretical analysis to support the experience from previous…
In this paper, based on a successively accuracy-increasing approximation of the $\ell_0$ norm, we propose a new algorithm for recovery of sparse vectors from underdetermined measurements. The approximations are realized with a certain class…
This paper proposes an improved variable step-size (VSS) algorithm for the recently introduced affine projection sign algorithm (APSA) based on the recovery of the near-end signal energy in the error signal. Simulation results demonstrate…
We propose an efficient ADMM method with guarantees for high-dimensional problems. We provide explicit bounds for the sparse optimization problem and the noisy matrix decomposition problem. For sparse optimization, we establish that the…
Nonlinear adaptive filters often show some sparse behavior due to the fact that not all the coefficients are equally useful for the modeling of any nonlinearity. Recently, a class of proportionate algorithms has been proposed for nonlinear…
In this paper we discuss the variable selection method from \ell0-norm constrained regression, which is equivalent to the problem of finding the best subset of a fixed size. Our study focuses on two aspects, consistency and computation. We…
In this paper we consider solving \emph{noisy} under-determined systems of linear equations with sparse solutions. A noiseless equivalent attracted enormous attention in recent years, above all, due to work of…
In this paper, we investigate power-constrained sensing matrix design in a sparse Gaussian linear dimensionality reduction framework. Our study is carried out in a single--terminal setup as well as in a multi--terminal setup consisting of…
Recently, the leaky diffusion least-mean-square (DLMS) algorithm has obtained much attention because of its good performance for high input eigenvalue spread and low signal-to-noise ratio (SNR). However, the leaky DLMS algorithm may suffer…
High-dimensional learning problems, where the number of features exceeds the sample size, often require sparse regularization for effective prediction and variable selection. While established for fully supervised data, these techniques…
We consider (nonparametric) sparse (generalized) additive models (SpAM) for classification. The design of a SpAM classifier is based on minimizing the logistic loss with a sparse group Lasso/Slope-type penalties on the coefficients of…
Conventional algorithms for sparse signal recovery and sparse representation rely on $l_1$-norm regularized variational methods. However, when applied to the reconstruction of $\textit{sparse images}$, i.e., images where only a few pixels…
We present the framework of slowly varying regression under sparsity, allowing sparse regression models to exhibit slow and sparse variations. The problem of parameter estimation is formulated as a mixed-integer optimization problem. We…
Large-scale sparse multi-objective optimization problems (LSMOPs) are prevalent in real-world applications, where optimal solutions typically contain only a few nonzero variables, such as in adversarial attacks, critical node detection, and…
High signal to noise ratio (SNR) consistency of model selection criteria in linear regression models has attracted a lot of attention recently. However, most of the existing literature on high SNR consistency deals with model order…
In this work, we consider a class of differentiable criteria for sparse image computing problems, where a nonconvex regularization is applied to an arbitrary linear transform of the target image. As special cases, it includes…