Related papers: Operator Shifting for General Noisy Matrix Systems

Motivated by a recently proposed error estimator for the transfer function of the reduced-order model of a given linear dynamical system, we further develop more theoretical results in this work. Furthermore, we propose several variants of…

Pose-Graph optimization is a crucial component of many modern SLAM systems. Most prominent state of the art systems address this problem by iterative non-linear least squares. Both number of iterations and convergence basin of these…

Elliptically symmetric distributions are a classic example of a semiparametric model where the location vector and the scatter matrix (or a parameterization of them) are the two finite-dimensional parameters of interest, while the density…

This investigation is motivated by PDE-constrained optimization problems arising in connection with electrocardiograms (ECGs) and electroencephalography (EEG). Standard sparsity regularization does not necessarily produce adequate results…

This paper considers the problem of matrix completion when the observed entries are noisy and contain outliers. It begins with introducing a new optimization criterion for which the recovered matrix is defined as its solution. This…

The potential of employing higher orders of the Trotter-Suzuki decomposition of the evolution operator for more effective simulations of quantum systems on a noisy quantum computer is explored. By examining the transverse-field Ising model…

We investigate the problem of estimating a given real symmetric signal matrix $\textbf{C}$ from a noisy observation matrix $\textbf{M}$ in the limit of large dimension. We consider the case where the noisy measurement $\textbf{M}$ comes…

We propose a unified framework for estimating low-rank matrices through nonconvex optimization based on gradient descent algorithm. Our framework is quite general and can be applied to both noisy and noiseless observations. In the general…

Despite the importance of denoising in modern machine learning and ample empirical work on supervised denoising, its theoretical understanding is still relatively scarce. One concern about studying supervised denoising is that one might not…

In machine learning models, the estimation of errors is often complex due to distribution bias, particularly in spatial data such as those found in environmental studies. We introduce an approach based on the ideas of importance sampling to…

It is well-understood that the robustness of mechanical and robotic control systems depends critically on minimizing sensitivity to arbitrary application-specific details whenever possible. For example, if a system is defined and performs…

We study a class of statistical inverse problems with non-linear pointwise operators motivated by concrete statistical applications. A two-step procedure is proposed, where the first step smoothes the data and inverts the non-linearity.…

This paper introduces an efficient algorithm for computing the general oscillatory matrix functions. These computations are crucial for solving second-order semi-linear initial value problems. The method is exploited using the scaling and…

This work proposes a universal and adaptive second-order method for minimizing second-order smooth, convex functions. Our algorithm achieves $O(\sigma / \sqrt{T})$ convergence when the oracle feedback is stochastic with variance $\sigma^2$,…

Quantization has become a predominant approach for model compression, enabling deployment of large models trained on GPUs onto smaller form-factor devices for inference. Quantization-aware training (QAT) optimizes model parameters with…

We consider variational inequalities coming from monotone operators, a setting that includes convex minimization and convex-concave saddle-point problems. We assume an access to potentially noisy unbiased values of the monotone operators…

This paper describes recursive algorithms for state estimation of linear dynamical systems when measurements are noisy with unknown bias and/or outliers. For situations with noisy and biased measurements, algorithms are proposed that…

Microwave imaging is commonly based on the solution of linearized inverse scattering problems by matched filtering algorithms, i.e., by applying the adjoint of the forward scattering operator to the observation data. A more rigorous…

We consider the problem of performing inverse reinforcement learning when the trajectory of the expert is not perfectly observed by the learner. Instead, a noisy continuous-time observation of the trajectory is provided to the learner. This…

An algorithm is proposed, analyzed, and tested for minimizing locally Lipschitz objective functions that may be nonconvex and/or nonsmooth. The algorithm, which is built upon the gradient-sampling methodology, is designed specifically for…