Related papers: Dantzig Selector with an Approximately Optimal Den…
In this paper, we develop a randomized algorithm and theory for learning a sparse model from large-scale and high-dimensional data, which is usually formulated as an empirical risk minimization problem with a sparsity-inducing regularizer.…
In this paper we present two new approaches to efficiently solve large-scale compressed sensing problems. These two ideas are independent of each other and can therefore be used either separately or together. We consider all possibilities.…
We present a dynamic programming algorithm for selecting a representative subset of size $k$ from a given set with $n$ points such that the Riesz $s$-energy is near minimized. While NP-hard in general dimensions, the one-dimensional case…
For consistency (even oracle properties) of estimation and model prediction, almost all existing methods of variable/feature selection critically depend on sparsity of models. However, for ``large $p$ and small $n$" models sparsity…
Variable selection plays an important role in high dimensional statistical modeling which nowadays appears in many areas and is key to various scientific discoveries. For problems of large scale or dimensionality $p$, estimation accuracy…
We propose a Generalized Dantzig Selector (GDS) for linear models, in which any norm encoding the parameter structure can be leveraged for estimation. We investigate both computational and statistical aspects of the GDS. Based on conjugate…
Generalized inverses play a fundamental role in numerical linear algebra, particularly when matrices are rectangular, singular, or rank deficient. Even when the input matrix is sparse, generalized inverses such as the M-P pseudoinverse are…
Deep neural networks have emerged as powerful tools for learning operators defined over infinite-dimensional function spaces. However, existing theories frequently encounter difficulties related to dimensionality and limited…
Interpretation of Deep Neural Networks (DNNs) training as an optimal control problem with nonlinear dynamical systems has received considerable attention recently, yet the algorithmic development remains relatively limited. In this work, we…
An algorithmic framework, based on the difference of convex functions algorithm (DCA), is proposed for minimizing a class of concave sparse metrics for compressed sensing problems. The resulting algorithm iterates a sequence of $\ell_1$…
Orthogonal time frequency space (OTFS) modulation is a two-dimensional modulation scheme designed in the delay-Doppler (DD) domain, exhibiting superior performance over orthogonal frequency division multiplexing (OFDM) modulation in…
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…
We develop a data-driven optimal shrinkage algorithm for matrix denoising in the presence of high-dimensional noise with a separable covariance structure; that is, the noise is colored and dependent across samples. The algorithm, coined…
With the decreasing cost of data collection, the space of variables or features that can be used to characterize a particular predictor of interest continues to grow exponentially. Therefore, identifying the most characterizing features…
Matroid intersection is a classical optimization problem where, given two matroids over the same ground set, the goal is to find the largest common independent set. In this paper, we show that there exists a certain "sparsifer": a subset of…
Micro-Doppler analysis has become increasingly popular in recent years owning to the ability of the technique to enhance classification strategies. Applications include recognising everyday human activities, distinguishing drone from birds,…
Optimizing the acquisition matrix is useful for compressed sensing of signals that are sparse in overcomplete dictionaries, because the acquisition matrix can be adapted to the particular correlations of the dictionary atoms. In this paper…
Sparse tensors are prevalent in many data-intensive applications, yet existing differentiable programming frameworks are tailored towards dense tensors. This presents a significant challenge for efficiently computing gradients through…
Detection of a signal under noise is a classical signal processing problem. When monitoring spatial phenomena under a fixed budget, i.e., either physical, economical or computational constraints, the selection of a subset of available…
The estimation of a sparse vector in the linear model is a fundamental problem in signal processing, statistics, and compressive sensing. This paper establishes a lower bound on the mean-squared error, which holds regardless of the…