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In this work, we develop new optimization algorithms that use approximate second-order information combined with the gradient regularization technique to achieve fast global convergence rates for both convex and non-convex objectives. The…
For the accurate representation and reconstruction of band-limited signals on the sphere, an optimal-dimensionality sampling scheme has been recently proposed which requires the optimal number of samples equal to the number of degrees of…
In many real-world problems, we are dealing with collections of high-dimensional data, such as images, videos, text and web documents, DNA microarray data, and more. Often, high-dimensional data lie close to low-dimensional structures…
We present a new computational approach to approximating a large, noisy data table by a low-rank matrix with sparse singular vectors. The approximation is obtained from thresholded subspace iterations that produce the singular vectors…
Sparsity-constrained optimization underlies many problems in signal processing, statistics, and machine learning. State-of-the-art hard-thresholding (HT) algorithms rely on an appropriately selected continuous step-size parameter to ensure…
Deep neural networks (DNNs) have shown great success in many machine learning tasks. Their training is challenging since the loss surface of the network architecture is generally non-convex, or even non-smooth. How and under what…
For uncertainty propagation of highly complex and/or nonlinear problems, one must resort to sample-based non-intrusive approaches [1]. In such cases, minimizing the number of function evaluations required to evaluate the response surface is…
Stochastic gradient descent (SGD) provides a simple and efficient way to solve a broad range of machine learning problems. Here, we focus on distribution regression (DR), involving two stages of sampling: Firstly, we regress from…
The 3D Gaussian splatting methods are getting popular. However, they work directly on the signal, leading to a dense representation of the signal. Even with some techniques such as pruning or distillation, the results are still dense. In…
A recent trend in the signal/image processing literature is the optimization of Fourier sampling schemes for specific datasets of signals. In this paper, we explain why choosing optimal non Cartesian Fourier sampling patterns is a difficult…
Quantum simulation, the simulation of quantum processes on quantum computers, suggests a path forward for the efficient simulation of problems in condensed-matter physics, quantum chemistry, and materials science. While the majority of…
To accelerate kernel methods, we propose a near input sparsity time algorithm for sampling the high-dimensional feature space implicitly defined by a kernel transformation. Our main contribution is an importance sampling method for…
We conducted an extensive computational experiment, lasting multiple CPU-years, to optimally select parameters for two important classes of algorithms for finding sparse solutions of underdetermined systems of linear equations. We make the…
We propose a novel sparse spectrum approximation of Gaussian process (GP) tailored for Bayesian optimization. Whilst the current sparse spectrum methods provide desired approximations for regression problems, it is observed that this…
A new gradient-based adaptive sampling method is proposed for design of experiments applications which balances space filling, local refinement, and error minimization objectives while reducing reliance on delicate tuning parameters. High…
Motivated by the need for efficient estimation of conditional expectations, we consider a least-squares function approximation problem with heavily polluted data. Existing methods that are effective in the small-noise regime are suboptimal…
In this work, we deal with the problem of computing a comprehensive front of efficient solutions in multi-objective portfolio optimization problems in presence of sparsity constraints. We start the discussion pointing out some weaknesses of…
This paper proposes a stochastic gradient descent method with an adaptive Gaussian noise term for the global minimization of nearly convex functions, which are nonconvex and possess multiple strict local minimizers. The noise term,…
We present a new modeling paradigm for optimization that we call random field optimization. Random fields are a powerful modeling abstraction that aims to capture the behavior of random variables that live on infinite-dimensional spaces…
In this work, we propose a method for determining a non-uniform sampling scheme for multi-dimensional signals by solving a convex optimization problem reminiscent of the sensor selection problem. The resulting sampling scheme minimizes the…