Related papers: Splitting Method for Support Vector Machine in Rep…

Consider linear ill-posed problems governed by the system $A_i x = y_i$ for $i =1, \cdots, p$, where each $A_i$ is a bounded linear operator from a Banach space $X$ to a Hilbert space $Y_i$. In case $p$ is huge, solving the problem by an…

We prove results on weak convergence for the alternating split Bregman algorithm in infinite dimensional Hilbert spaces. We also show convergence of an approximate split Bregman algorithm, where errors are allowed at each step of the…

A class of splitting alternating algorithms is proposed for finding the sparse solution of linear systems with concatenated orthogonal matrices. Depending on the number of matrices concatenated, the proposed algorithms are classified into…

Distributed computing systems are well-known to suffer from the problem of slow or failed nodes; these are referred to as stragglers. Straggler mitigation (for distributed matrix computations) has recently been investigated from the…

We explore an explicit link between stochastic gradient descent using common batching strategies and splitting methods for ordinary differential equations. From this perspective, we introduce a new minibatching strategy (called Symmetric…

We study the sparse recovery problem with an underdetermined linear system characterized by a Kronecker-structured dictionary and a Kronecker-supported sparse vector. We cast this problem into the sparse Bayesian learning (SBL) framework…

In this paper, we propose variants of forward-backward splitting method for solving the system of splitting inclusion problem. We propose a conceptual algorithm containing three variants, each having a different projection steps. The…

In this paper, we study a class of nonconvex and nonsmooth structured difference-of-convex (DC) programs, which contain in the convex part the sum of a nonsmooth linearly composed convex function and a differentiable function, and in the…

The Nystr\"om methods have been popular techniques for scalable kernel based learning. They approximate explicit, low-dimensional feature mappings for kernel functions from the pairwise comparisons with the training data. However, Nystr\"om…

This paper presents an iterative method suitable for inverting semilinear problems which are important kernels in many numerical applications. The primary idea is to employ a parametrization that is able to reduce semilinear problems into…

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 paper we introduce a novel method for segmentation that can benefit from general semantics of Convolutional Neural Network (CNN). Our segmentation proposes visually and semantically coherent image segments. We use binary encoding of…

Reproducing kernel Hilbert spaces provide a foundational framework for kernel-based learning, where regularization and interpolation problems admit finite-dimensional solutions through classical representer theorems. Many modern learning…

We present a novel method for graph partitioning, based on reinforcement learning and graph convolutional neural networks. Our approach is to recursively partition coarser representations of a given graph. The neural network is implemented…

Improvement of statistical learning models in order to increase efficiency in solving classification or regression problems is still a goal pursued by the scientific community. In this way, the support vector machine model is one of the…

The use of deep learning models in computational biology has increased massively in recent years, and it is expected to continue with the current advances in the fields such as Natural Language Processing. These models, although able to…

We introduce a new loss function for the weakly-supervised training of semantic image segmentation models based on three guiding principles: to seed with weak localization cues, to expand objects based on the information about which classes…

End-to-end weakly supervised semantic segmentation aims at optimizing a segmentation model in a single-stage training process based on only image annotations. Existing methods adopt an online-trained classification branch to provide pseudo…

We analyze a binary classification problem by using a support vector machine based on variational quantum-circuit model. We propose to solve a linear equation of the support vector machine by using a $\Gamma$ matrix expansion. In addition,…

Although support vector machines (SVMs) are theoretically well understood, their underlying optimization problem becomes very expensive, if, for example, hundreds of thousands of samples and a non-linear kernel are considered. Several…