Related papers: Expanding boundaries of Gap Safe screening
This paper concerns models and convergence principles for dealing with stochasticity in a wide range of algorithms arising in nonlinear analysis and optimization in Hilbert spaces. It proposes a flexible geometric framework within which…
Contact-implicit motion planning-embedding contact sequencing as implicit complementarity constraints-holds the promise of leveraging continuous optimization to discover new contact patterns online. Nevertheless, the resulting optimization,…
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…
Sparse signal reconstruction algorithms have attracted research attention due to their wide applications in various fields. In this paper, we present a simple Bayesian approach that utilizes the sparsity constraint and a priori statistical…
Sparse ridge regression is widely utilized in modern data analysis and machine learning. However, computing globally optimal solutions for sparse ridge regression is challenging, particularly when samples are arbitrarily given or generated…
Computed Tomography (CT) is a prominent example of Imaging Inverse Problem highlighting the unrivaled performances of data-driven methods in degraded measurements setups like sparse X-ray projections. Although a significant proportion of…
Modern statistical applications often involve minimizing an objective function that may be nonsmooth and/or nonconvex. This paper focuses on a broad Bregman-surrogate algorithm framework including the local linear approximation, mirror…
Binary optimization is a central problem in mathematical optimization and its applications are abundant. To solve this problem, we propose a new class of continuous optimization techniques which is based on Mathematical Programming with…
Regularization is a common tool in variational inverse problems to impose assumptions on the parameters of the problem. One such assumption is sparsity, which is commonly promoted using lasso and total variation-like regularization.…
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…
Neural networks achieve strong empirical performance, but robustness concerns still hinder deployment in safety-critical applications. Formal verification provides robustness guarantees, but current methods face a scalability-completeness…
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…
Dense conditional random fields (CRF) with Gaussian pairwise potentials have emerged as a popular framework for several computer vision applications such as stereo correspondence and semantic segmentation. By modeling long-range…
Gradient clipping is commonly used in training deep neural networks partly due to its practicability in relieving the exploding gradient problem. Recently, \citet{zhang2019gradient} show that clipped (stochastic) Gradient Descent (GD)…
This paper addresses the task of estimating a covariance matrix under a patternless sparsity assumption. In contrast to existing approaches based on thresholding or shrinkage penalties, we propose a likelihood-based method that regularizes…
Spreading the information over all coefficients of a representation is a desirable property in many applications such as digital communication or machine learning. This so-called antisparse representation can be obtained by solving a convex…
The use of high-dimensional features has become a normal practice in many computer vision applications. The large dimension of these features is a limiting factor upon the number of data points which may be effectively stored and processed,…
We study the problem of constrained efficient global optimization, where both the objective and constraints are expensive black-box functions that can be learned with Gaussian processes. We propose CONFIG (CONstrained efFIcient Global…
Structured sparse optimization is an important and challenging problem for analyzing high-dimensional data in a variety of applications such as bioinformatics, medical imaging, social networks, and astronomy. Although a number of structured…
Matrix form data sets arise in many areas, so there are lots of works about the matrix regression models. One special model of these models is the adaptive nuclear norm regularized trace regression, which has been proven have good…