Related papers: Computing a Sparse Approximate Inverse on Quantum …
We solve the analysis sparse coding problem considering a combination of convex and non-convex sparsity promoting penalties. The multi-penalty formulation results in an iterative algorithm involving proximal-averaging. We then unfold the…
We consider the problem of finding a sparse solution for an underdetermined linear system of equations when the known parameters on both sides of the system are subject to perturbation. This problem is particularly relevant to…
Proximal gradient methods are popular in sparse optimization as they are straightforward to implement. Nevertheless, they achieve biased solutions, requiring many iterations to converge. This work addresses these issues through a suitable…
Surrogate models are used to alleviate the computational burden in engineering tasks, which require the repeated evaluation of computationally demanding models of physical systems, such as the efficient propagation of uncertainties. For…
Charged particle reconstruction or track reconstruction is one of the most crucial components of pattern recognition in high-energy collider physics. It is known to entail enormous consumption of computing resources, especially when the…
High dimensional covariance estimation and graphical models is a contemporary topic in statistics and machine learning having widespread applications. An important line of research in this regard is to shrink the extreme spectrum of the…
Sparse Principal Component Analysis (sparse PCA) is a fundamental dimension-reduction tool that enhances interpretability in various high-dimensional settings. An important variant of sparse PCA studies the scenario when samples are…
We introduce a variational algorithm based on the quantum alternating operator ansatz (QAOA) for the approximate solution of computationally hard counting problems. Our algorithm, dubbed VQCount, is based on the equivalence between random…
We consider the maximum likelihood estimation of sparse inverse covariance matrices. We demonstrate that current heuristic approaches primarily encourage robustness, instead of the desired sparsity. We give a novel approach that solves the…
We propose a novel method for reducing the number of variables in quadratic unconstrained binary optimization problems, using a quantum annealer (or any sampler) to fix the value of a large portion of the variables to values that have a…
We consider the problem of estimating sparse graphs by a lasso penalty applied to the inverse covariance matrix. Using a coordinate descent procedure for the lasso, we develop a simple algorithm that is remarkably fast: in the worst cases,…
Search-based software engineering (SBSE) addresses critical optimization challenges in software engineering, including the next release problem (NRP) and feature selection problem (FSP). While traditional heuristic approaches and integer…
This work proposes an adaptive sequential Monte Carlo sampling algorithm to solve Bayesian inverse problems in scenarios where likelihood evaluations are costly but can be approximated using a surrogate model built from previous evaluations…
We study efficient algorithms for Sparse PCA in standard statistical models (spiked covariance in its Wishart form). Our goal is to achieve optimal recovery guarantees while being resilient to small perturbations. Despite a long history of…
We propose a new method for solving binary optimization problems under inequality constraints using a quantum annealer. To deal with inequality constraints, we often use slack variables, as in previous approaches. When we use slack…
We consider (nonparametric) sparse (generalized) additive models (SpAM) for classification. The design of a SpAM classifier is based on minimizing the logistic loss with a sparse group Lasso/Slope-type penalties on the coefficients of…
How can we compute the pseudoinverse of a sparse feature matrix efficiently and accurately for solving optimization problems? A pseudoinverse is a generalization of a matrix inverse, which has been extensively utilized as a fundamental…
The quantum approximate optimization algorithm (QAOA) is a hybrid quantum-classical variational algorithm that offers the potential to handle combinatorial optimization problems. Introducing constraints in such combinatorial optimization…
In high-dimensional settings, sparse structures are critical for efficiency in term of memory and computation complexity. For a linear system, to find the sparsest solution provided with an over-complete dictionary of features directly is…
We consider the problem of sparse atomic optimization, where the notion of "sparsity" is generalized to meaning some linear combination of few atoms. The definition of atomic set is very broad; popular examples include the standard basis,…