相关论文: Gradient Support Projection Algorithm for Affine F…

We study convergence of the iterative projected gradient (IPG) algorithm for arbitrary (possibly nonconvex) sets and when both the gradient and projection oracles are computed approximately. We consider different notions of approximation of…

With the excellent accuracy and feasibility, the Neural Networks have been widely applied into the novel intelligent applications and systems. However, with the appearance of the Adversarial Attack, the NN based system performance becomes…

Sparse subspace clustering (SSC) clusters $n$ points that lie near a union of low-dimensional subspaces. The SSC model expresses each point as a linear or affine combination of the other points, using either $\ell_1$ or $\ell_0$…

This paper provides the first tight convergence analyses for RMSProp and Adam in non-convex optimization under the most relaxed assumptions of coordinate-wise generalized smoothness and affine noise variance. We first analyze RMSProp, which…

This paper studies the sparsistency and rates of convergence for estimating sparse covariance and precision matrices based on penalized likelihood with nonconvex penalty functions. Here, sparsistency refers to the property that all…

A unified linear algebraic approach to adaptive signal processing (ASP) is presented. Starting from just Ax=b, key ASP algorithms are derived in a simple, systematic, and integrated manner without requiring any background knowledge to the…

The random feature method (RFM), a mesh-free machine learning-based framework, has emerged as a promising alternative for solving PDEs on complex domains. However, for large three-dimensional nonlinear problems, attaining high accuracy…

By drawing on ideas from optimisation theory, artificial neural networks (ANN), graph embeddings and sparse representations, I develop a novel technique, termed SENNS (Sparse Extraction Neural NetworkS), aimed at addressing the feature…

In this paper, we show that the adaptive projected subgradient method (APSM) is bounded perturbation resilient. To illustrate a potential application of this result, we propose a set-theoretic framework for MIMO detection, and we devise…

Sparse coding has achieved a great success in various image processing studies. However, there is not any benchmark to measure the sparsity of image patch/group because sparse discriminant conditions cannot keep unchanged. This paper…

It is a common practice to exploit pyramidal feature representation to tackle the problem of scale variation in object instances. However, most of them still predict the objects in a certain range of scales based solely or mainly on a…

Spiking Neural Networks (SNNs) have attracted great attention for their energy-efficient operations and biologically inspired structures, offering potential advantages over Artificial Neural Networks (ANNs) in terms of energy efficiency and…

We consider minimizing finite-sum and expectation objective functions via Hessian-averaging based subsampled Newton methods. These methods allow for gradient inexactness and have fixed per-iteration Hessian approximation costs. The recent…

A recursive algorithm named Zero-point Attracting Projection (ZAP) is proposed recently for sparse signal reconstruction. Compared with the reference algorithms, ZAP demonstrates rather good performance in recovery precision and robustness.…

Information processing techniques based on sparseness have been actively studied in several disciplines. Among them, a mathematical framework to approximately express a given dataset by a combination of a small number of basis vectors of an…

Generative Adversarial Networks (GANs) are an unsupervised generative model that learns data distribution through adversarial training. However, recent experiments indicated that GANs are difficult to train due to the requirement of…

We consider constrained minimization problems and propose to replace the projection onto the entire feasible region, required in the Projected Subgradient Method (PSM), by projections onto the individual sets whose intersection forms the…

Sparsity promoting functions (SPFs) are commonly used in optimization problems to find solutions which are assumed or desired to be sparse in some basis. For example, the l1-regularized variation model and the Rudin-Osher-Fatemi total…

In this work we explore the fundamental structure-adaptiveness of state of the art randomized first order algorithms on regularized empirical risk minimization tasks, where the solution has intrinsic low-dimensional structure (such as…

Sparse regression and classification estimators that respect group structures have application to an assortment of statistical and machine learning problems, from multitask learning to sparse additive modeling to hierarchical selection.…