Related papers: skscope: Fast Sparsity-Constrained Optimization in…
Recently dictionary screening has been proposed as an effective way to improve the computational efficiency of solving the lasso problem, which is one of the most commonly used method for learning sparse representations. To address today's…
Random projection, a dimensionality reduction technique, has been found useful in recent years for reducing the size of optimization problems. In this paper, we explore the use of sparse sub-gaussian random projections to approximate…
Sparse linear iterative solvers are essential for many large-scale simulations. Much of the runtime of these solvers is often spent in the implicit evaluation of matrix polynomials via a sequence of sparse matrix-vector products. A variety…
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…
Inversion codes are numerical tools used for the inference of physical properties from the observations. Despite their success, the quality of current spectropolarimetric observations and those expected in the near future presents a…
Minimizing sum of two functions under a linear constraint is what we called splitting problem. This convex optimization has wide applications in machine learning problems, such as Lasso, Group Lasso and Sparse logistic regression. A recent…
The Julia library TSSOS aims at helping polynomial optimizers to solve large-scale problems with sparse input data. The underlying algorithmic framework is based on exploiting correlative and term sparsity to obtain a new moment-SOS…
We formulate the loop-free, binary superoptimization task as a stochastic search problem. The competing constraints of transformation correctness and performance improvement are encoded as terms in a cost function, and a Markov Chain Monte…
Sparse linear algebra is a cornerstone of many scientific computing and machine learning applications. Python has become a popular choice for these applications due to its simplicity and ease of use. Yet high performance sparse kernels in…
Sparse linear system solvers are computationally expensive kernels that lie at the heart of numerous applications. This paper proposes a flexible preconditioning framework to substantially reduce the time and energy requirements of this…
The rapid development of computation power and machine learning algorithms has paved the way for automating scientific discovery with a scanning probe microscope (SPM). The key elements towards operationalization of automated SPM are the…
In this paper, we investigate the necessity of traceability for accurate learning in stochastic convex optimization (SCO) under $\ell_p$ geometries. Informally, we say a learning algorithm is $m$-traceable if, by analyzing its output, it is…
We present a generic coordinate descent solver for the minimization of a nonsmooth convex objective with structure. The method can deal in particular with problems with linear constraints. The implementation makes use of efficient residual…
This paper studies the copositive optimization problem whose objective is a sparse polynomial, with linear constraints over the nonnegative orthant. We propose sparse Moment-SOS relaxations to solve it. Necessary and sufficient conditions…
Spline functions are smooth piecewise polynomials widely used for interpolation and smoothing, and nonnegative spline smoothing is also studied for nonnegative data. Previous research used sufficient conditions for the nonnegativity of…
Recently, the prediction-correction method has been developed to solve nonlinear convex optimization problems. However, its convergence rate is often poor since large regularization parameters are set to ensure convergence conditions. In…
There is a recent surge of interest in developing algorithms for finding sparse solutions of underdetermined systems of linear equations $y = \Phi x$. In many applications, extremely large problem sizes are envisioned, with at least tens of…
The Standard Quadratic optimization Problem (StQP), arguably the simplest among all classes of NP-hard optimization problems, consists of extremizing a quadratic form (the simplest nonlinear polynomial) over the standard simplex (the…
Classifiers based on sparse representations have recently been shown to provide excellent results in many visual recognition and classification tasks. However, the high cost of computing sparse representations at test time is a major…
An improved version of the sparse multiway kernel spectral clustering (KSC) is presented in this brief. The original algorithm is derived from weighted kernel principal component (KPCA) analysis formulated within the primal-dual…