Related papers: Analysis of Truncated Orthogonal Iteration for Spa…

Orthogonal matching pursuit~(OMP) is a commonly used greedy algorithm for recovering sparse signals from compressed measurements. In this paper, we introduce a variant of the OMP algorithm to reduce the complexity of reconstructing a class…

In this paper we propose a computationally efficient algorithm for on-line variable selection in multivariate regression problems involving high dimensional data streams. The algorithm recursively extracts all the latent factors of a…

Sparse coding--that is, modelling data vectors as sparse linear combinations of basis elements--is widely used in machine learning, neuroscience, signal processing, and statistics. This paper focuses on the large-scale matrix factorization…

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…

We propose sparseGeoHOPCA, a novel framework for sparse higher-order principal component analysis (SHOPCA) that introduces a geometric perspective to high-dimensional tensor decomposition. By unfolding the input tensor along each mode and…

We propose sparse regression as an alternative to neural networks for the discovery of parsimonious constitutive models (CMs) from oscillatory shear experiments. Symmetry and frame-invariance are strictly imposed by using tensor basis…

Computing more than one eigenvalue for (large sparse) one-parameter polynomial and general nonlinear eigenproblems, as well as for multiparameter linear and nonlinear eigenproblems, is a much harder task than for standard eigenvalue…

The need for fast sparse optimization is emerging, e.g., to deal with large-dimensional data-driven problems and to track time-varying systems. In the framework of linear sparse optimization, the iterative shrinkage-thresholding algorithm…

Sparse phase retrieval plays an important role in many fields of applied science and thus attracts lots of attention. In this paper, we propose a \underline{sto}chastic alte\underline{r}nating \underline{m}inimizing method for…

Random sinusoidal features are a popular approach for speeding up kernel-based inference in large datasets. Prior to the inference stage, the approach suggests performing dimensionality reduction by first multiplying each data vector by a…

Is it possible to find the sparsest vector (direction) in a generic subspace $\mathcal{S} \subseteq \mathbb{R}^p$ with $\mathrm{dim}(\mathcal{S})= n < p$? This problem can be considered a homogeneous variant of the sparse recovery problem,…

In this article, we consider the sparse tensor singular value decomposition, which aims for dimension reduction on high-dimensional high-order data with certain sparsity structure. A method named Sparse Tensor Alternating Thresholding for…

We consider the sparse principal component analysis for high-dimensional stationary processes. The standard principal component analysis performs poorly when the dimension of the process is large. We establish the oracle inequalities for…

This paper studies the problem of Kronecker-structured sparse vector recovery from an underdetermined linear system with a Kronecker-structured dictionary. Such a problem arises in many real-world applications such as the sparse channel…

Non-convex constraints have recently proven a valuable tool in many optimisation problems. In particular sparsity constraints have had a significant impact on sampling theory, where they are used in Compressed Sensing and allow structured…

The question of fast convergence in the classical problem of high dimensional linear regression has been extensively studied. Arguably, one of the fastest procedures in practice is Iterative Hard Thresholding (IHT). Still, IHT relies…

In this paper, a multi-parameterized proximal point algorithm combining with a relaxation step is developed for solving convex minimization problem subject to linear constraints. We show its global convergence and sublinear convergence rate…

Principal component analysis (PCA) is a widely used dimension reduction technique in machine learning and multivariate statistics. To improve the interpretability of PCA, various approaches to obtain sparse principal direction loadings have…

In sparse coding, we attempt to extract features of input vectors, assuming that the data is inherently structured as a sparse superposition of basic building blocks. Similarly, neural networks perform a given task by learning features of…

Given a sample covariance matrix, we examine the problem of maximizing the variance explained by a linear combination of the input variables while constraining the number of nonzero coefficients in this combination. This is known as sparse…