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We propose a greedy algorithm to select $N$ important features among $P$ input features for a non-linear prediction problem. The features are selected one by one sequentially, in an iterative loss minimization procedure. We use neural…

Dimensionality reduction on quadratic manifolds augments linear approximations with quadratic correction terms. Previous works rely on linear approximations given by projections onto the first few leading principal components of the…

With a greedy strategy to construct control index set of coordinates firstly and then choosing the corresponding column submatrix in each iteration, we present a greedy block Gauss-Seidel (GBGS) method for solving large linear least squares…

Block coordinate descent (BCD) methods are prevalent in large scale optimization problems due to the low memory and computational costs per iteration, the predisposition to parallelization, and the ability to exploit the structure of the…

We extend some rate of convergence results of greedy quantization sequences already investigated in arXiv:1409.0732 [math.PR]. We show, for a more general class of distributions satisfying a certain control, that the quantization error of…

Gradient descent (GD) methods are commonly employed in machine learning problems to optimize the parameters of the model in an iterative fashion. For problems with massive datasets, computations are distributed to many parallel computing…

Large-scale sparse precision matrix estimation has attracted wide interest from the statistics community. The convex partial correlation selection method (CONCORD) developed by Khare et al. (2015) has recently been credited with some…

Parameterized quantum circuits (PQCs) are ubiquitous in the design of hybrid quantum-classical algorithms. In this work, we propose an interpolation-based coordinate descent (ICD) method to address the parameter optimization problem in…

We present a coordinate ascent method for a class of semidefinite programming problems that arise in non-convex quadratic integer optimization. These semidefinite programs are characterized by a small total number of active constraints and…

The state-of-the-art methods for solving optimization problems in big dimensions are variants of randomized coordinate descent (RCD). In this paper we introduce a fundamentally new type of acceleration strategy for RCD based on the…

In recent studies on sparse modeling, $l_q$ ($0<q<1$) regularization has received considerable attention due to its superiorities on sparsity-inducing and bias reduction over the $l_1$ regularization.In this paper, we propose a cyclic…

The use of Quantum Neural Networks (QNN) that are analogous to classical neural networks, has greatly increased in the past decade owing to the growing interest in the field of Quantum Machine Learning (QML). A QNN consists of three major…

We propose a random coordinate descent algorithm for optimizing a non-convex objective function subject to one linear constraint and simple bounds on the variables. Although it is common use to update only two random coordinates…

Many network applications can be formulated as NP-hard combinatorial optimization problems of community detection (CD). Due to the NP-hardness, to balance the CD quality and efficiency remains a challenge. Most existing CD methods are…

Mean-reverting portfolios with few assets, but high variance, are of great interest for investors in financial markets. Such portfolios are straightforwardly profitable because they include a small number of assets whose prices not only…

This work deals with tailored reduced order models for bifurcating nonlinear parametric partial differential equations, where multiple coexisting solutions arise for a given parametric instance. Approaches based on proper orthogonal…

Coordinate descent algorithms solve optimization problems by successively performing approximate minimization along coordinate directions or coordinate hyperplanes. They have been used in applications for many years, and their popularity…

Machine learning models can leak information about the data used to train them. To mitigate this issue, Differentially Private (DP) variants of optimization algorithms like Stochastic Gradient Descent (DP-SGD) have been designed to…

Projected Gradient Descent denotes a class of iterative methods for solving optimization programs. Its applicability to convex optimization programs has gained significant popularity for its intuitive implementation that involves only…

MAXCUT defines a classical NP-hard problem for graph partitioning and it serves as a typical case of the symmetric non-monotone Unconstrained Submodular Maximization (USM) problem. Applications of MAXCUT are abundant in machine learning,…