Related papers: Deflation-Free Optimal Scoring

We consider the problem of minimizing a high-dimensional objective function, which may include a regularization term, using (possibly noisy) evaluations of the function. Such optimization is also called derivative-free, zeroth-order, or…

Deflation techniques are typically used to shift isolated clusters of small eigenvalues in order to obtain a tighter distribution and a smaller condition number. Such changes induce a positive effect in the convergence behavior of Krylov…

In this paper, we consider a compressed sensing problem of reconstructing a sparse signal from an undersampled set of noisy linear measurements. The regularized least squares or least absolute shrinkage and selection operator (LASSO)…

We present a novel on-policy algorithm for solving stochastic optimal control (SOC) problems. By leveraging the Girsanov theorem, our method directly computes on-policy gradients of the SOC objective without expensive backpropagation…

In high-dimensional statistics, variable selection recovers the latent sparse patterns from all possible covariate combinations. This paper proposes a novel optimization method to solve the exact L0-regularized regression problem, which is…

In this paper, we review state-of-the-art methods for feature selection in statistics with an application-oriented eye. Indeed, sparsity is a valuable property and the profusion of research on the topic might have provided little guidance…

Sum of squares (SOS) optimization is a powerful technique for solving problems where the positivity of a polynomials must be enforced. The common approach to solve an SOS problem is by relaxation to a Semidefinite Program (SDP). The main…

The Sum-of-Squares (SOS) approximation method is a technique used in optimization problems to derive lower bounds on the optimal value of an objective function. By representing the objective function as a sum of squares in a feature space,…

In this manuscript, we analyze the sparse signal recovery (compressive sensing) problem from the perspective of convex optimization by stochastic proximal gradient descent. This view allows us to significantly simplify the recovery analysis…

Global polynomial optimization is an important tool across applied mathematics, with many applications in operations research, engineering, and physical sciences. In various settings, the polynomials depend on external parameters that may…

A sparse modeling is a major topic in machine learning and statistics. LASSO (Least Absolute Shrinkage and Selection Operator) is a popular sparse modeling method while it has been known to yield unexpected large bias especially at a sparse…

We provide a new hierarchy of semidefinite programming relaxations, called NCTSSOS, to solve large-scale sparse noncommutative polynomial optimization problems. This hierarchy features the exploitation of term sparsity hidden in the input…

We study the performance of sparse regression methods and propose new techniques to distill the governing equations of dynamical systems from data. We first look at the generic methodology of learning interpretable equation forms from data,…

Although cluttered indoor scenes have a lot of useful high-level semantic information which can be used for mapping and localization, most Visual Odometry (VO) algorithms rely on the usage of geometric features such as points, lines and…

Many real-world optimization problems contain parameters that are unknown before deployment time, either due to stochasticity or to lack of information (e.g., demand or travel times in delivery problems). A common strategy in such cases is…

Tilt-series alignment is crucial to obtaining high-resolution reconstructions in cryo-electron tomography. Beam-induced local deformation of the sample is hard to estimate from the low-contrast sample alone, and often requires fiducial gold…

Adapting Vision-Language Models (VLMs) to new domains with few labeled samples remains a significant challenge due to severe overfitting and computational constraints. State-of-the-art solutions, such as low-rank reparameterization,…

The lasso is the most famous sparse regression and feature selection method. One reason for its popularity is the speed at which the underlying optimization problem can be solved. Sorted L-One Penalized Estimation (SLOPE) is a…

Unsupervised feature selection (UFS) is widely applied in machine learning and pattern recognition. However, most of the existing methods only consider a single sparsity, which makes it difficult to select valuable and discriminative…

We present a novel method called TESALOCS (TEnsor SAmpling and LOCal Search) for multidimensional optimization, combining the strengths of gradient-free discrete methods and gradient-based approaches. The discrete optimization in our method…