Related papers: Designing Sampling Schemes for Multi-Dimensional D…
We propose a decomposition framework for the parallel optimization of the sum of a differentiable (possibly nonconvex) function and a (block) separable nonsmooth, convex one. The latter term is usually employed to enforce structure in the…
This paper focuses on radar waveform optimization for minimizing the Cram\'er-Rao bound (CRB) in a multiple-input multiple-output (MIMO) radar system. In contrast to conventional approaches relying on semi-definite programming (SDP) and…
We investigate the feature compression of high-dimensional ridge regression using the optimal subsampling technique. Specifically, based on the basic framework of random sampling algorithm on feature for ridge regression and the A-optimal…
Fr\'echet regression has received considerable attention to model metric-space valued responses that are complex and non-Euclidean data, such as probability distributions and vectors on the unit sphere. However, existing Fr\'echet…
In this paper we analyze several new methods for solving nonconvex optimization problems with the objective function formed as a sum of two terms: one is nonconvex and smooth, and another is convex but simple and its structure is known.…
In this chapter, we discuss recent work on learning sparse approximations to high-dimensional functions on data, where the target functions may be scalar-, vector- or even Hilbert space-valued. Our main objective is to study how the…
We consider the bilevel optimisation approach proposed by De Los Reyes, Sch\"onlieb (2013) for learning the optimal parameters in a Total Variation (TV) denoising model featuring for multiple noise distributions. In applications, the use of…
We propose a novel algorithm for solving non-convex, nonlinear equality-constrained finite-sum optimization problems. The proposed algorithm incorporates an additional sampling strategy for sample size update into the well-known framework…
The use of multichannel data in line spectral estimation (or frequency estimation) is common for improving the estimation accuracy in array processing, structural health monitoring, wireless communications, and more. Recently proposed…
This work proposes a novel convex-non-convex formulation of the image segmentation and the image completion problems. The proposed approach is based on the minimization of a functional involving two distinct regularization terms: one…
There have been many works that focus on the sampling set design for a static graph signal, but few for time-varying graph signals (GS). In this paper, we concentrate on how to select vertices to sample and how to allocate the sampling…
We study the problem of selecting limited features to observe such that models trained on them can perform well simultaneously across multiple subpopulations. This problem has applications in settings where collecting each feature is…
This paper studies simultaneous feature selection and extraction in supervised and unsupervised learning. We propose and investigate selective reduced rank regression for constructing optimal explanatory factors from a parsimonious subset…
Reducing acquisition time is of fundamental importance in various imaging modalities. The concept of variable density sampling provides a nice framework to achieve this. It was justified recently from a theoretical point of view in the…
In this paper, we consider the problem of stochastic optimization, where the objective function is in terms of the expectation of a (possibly non-convex) cost function that is parametrized by a random variable. While the convergence speed…
We consider constrained optimization problems with a nonsmooth objective function in the form of mathematical expectation. The Sample Average Approximation (SAA) is used to estimate the objective function and variable sample size strategy…
We investigate the problem of scanning and prediction ("scandiction", for short) of multidimensional data arrays. This problem arises in several aspects of image and video processing, such as predictive coding, for example, where an image…
We consider a non-convex constrained Lagrangian formulation of a fundamental bi-criteria optimization problem for variable selection in statistical learning; the two criteria are a smooth (possibly) nonconvex loss function, measuring the…
We propose a decomposition framework for the parallel optimization of the sum of a differentiable {(possibly nonconvex)} function and a nonsmooth (possibly nonseparable), convex one. The latter term is usually employed to enforce structure…
Post-selection strategies have been proposed with the aim of amplifying weak signals, which may help to overcome detection thresholds associated with technical noise in high-precision measurements. Here we use an optical setup to…