Related papers: A Consistently Oriented Basis for Eigenanalysis: I…

Second-order Newton-type algorithms that leverage the exact Hessian or its approximation are central to solve nonlinear optimization problems. However, their applications in solving large-scale nonconvex problems are hindered by three…

We show several ways to round a real matrix to an integer one such that the rounding errors in all rows and columns as well as the whole matrix are less than one. This is a classical problem with applications in many fields, in particular,…

Understanding the orientation of geological structures is crucial for analyzing the complexity of the Earths' subsurface. For instance, information about geological structure orientation can be incorporated into local anisotropic…

Recently, a class of algorithms combining classical fixed point iterations with repeated random sparsification of approximate solution vectors has been successfully applied to eigenproblems with matrices as large as $10^{108} \times…

Two meta-evolutionary optimization strategies described in this paper accelerate the convergence of evolutionary programming algorithms while still retaining much of their ability to deal with multi-modal problems. The strategies, called…

Autoregressive models capture stochastic processes in which past realizations determine the generative distribution of new data; they arise naturally in a variety of industrial, biomedical, and financial settings. A key challenge when…

We study the problem of learning a tensor from a set of linear measurements. A prominent methodology for this problem is based on a generalization of trace norm regularization, which has been used extensively for learning low rank matrices,…

Sparse reduced rank regression is an essential statistical learning method. In the contemporary literature, estimation is typically formulated as a nonconvex optimization that often yields to a local optimum in numerical computation. Yet,…

Diffusion models achieve remarkable fidelity in image synthesis, yet precise control over their outputs for targeted editing remains challenging. A key step toward controllability is to identify interpretable directions in the model's…

We present EigenSafe, an operator-theoretic framework for safety assessment of learning-enabled stochastic systems. In many robotic applications, the dynamics are inherently stochastic due to factors such as sensing noise and environmental…

The Parareal algorithm allows to solve evolution problems exploiting parallelization in time. Its convergence and stability have been proved under the assumption of regular (smooth) inputs. We present and analyze here a new Parareal…

Surgeons' technical skill directly impacts patient outcomes. To date, the angular motion of the instruments has been largely overlooked in objective skill evaluation. To fill this gap, we have developed metrics for surgical skill evaluation…

This paper proposes a new algorithm, named Householder Dice (HD), for simulating dynamics on dense random matrix ensembles with translation-invariant properties. Examples include the Gaussian ensemble, the Haar-distributed random orthogonal…

Understanding the distributions of spectral estimators in low-rank random matrix models, also known as signal-plus-noise matrix models, is fundamentally important in various statistical learning problems, including network analysis, matrix…

The Intelligent Fault Diagnosis of rotating machinery currently proposes some captivating challenges. Although results achieved by artificial intelligence and deep learning constantly improve, this field is characterized by several open…

We introduce deterministic perturbation schemes for the recently proposed random directions stochastic approximation (RDSA) [17], and propose new first-order and second-order algorithms. In the latter case, these are the first second-order…

We present a novel approach for the inverse problem in electrical impedance tomography based on regularized quadratic regression. Our contribution introduces a new formulation for the forward model in the form of a nonlinear integral…

Iterative learning procedures are ubiquitous in machine learning and modern statistics. Regularision is typically required to prevent inflating the expected loss of a procedure in later iterations via the propagation of noise inherent in…

We examine a class of embeddings based on structured random matrices with orthogonal rows which can be applied in many machine learning applications including dimensionality reduction and kernel approximation. For both the…

Oriented object detection in remote sensing images is a challenging task due to objects being distributed in multi-orientation. Recently, end-to-end transformer-based methods have achieved success by eliminating the need for post-processing…