Related papers: Least-Squares Parameter Estimation for State-Space…
Stochastic inverse problems considered in this article consist of estimating the probability distributions of intrinsically random inputs of computer models. These estimations are based on observable outputs affected by model noise, and…
Over the past few years, trace regression models have received considerable attention in the context of matrix completion, quantum state tomography, and compressed sensing. Estimation of the underlying matrix from regularization-based…
We develop and analyze stochastic inexact Gauss-Newton methods for nonlinear least-squares problems and for nonlinear systems ofequations. Random models are formed using suitable sampling strategies for the matrices involved in the…
Reliable forward uncertainty quantification in engineering requires methods that account for aleatory and epistemic uncertainties. In many applications, epistemic effects arising from uncertain parameters and model form dominate prediction…
Least squares is by far the simplest and most commonly applied computational method in many fields. In almost all applications, the least squares objective is rarely the true objective. We account for this discrepancy by parametrizing the…
We consider state and parameter estimation for a dynamical system having both time-varying and time-invariant parameters. It has been shown that the robustness of the Markov Chain Monte Carlo (MCMC) algorithm for estimating time-invariant…
State-space models are used in a wide range of time series analysis formulations. Kalman filtering and smoothing are work-horse algorithms in these settings. While classic algorithms assume Gaussian errors to simplify estimation, recent…
Many recent problems in signal processing and machine learning such as compressed sensing, image restoration, matrix/tensor recovery, and non-negative matrix factorization can be cast as constrained optimization. Projected gradient descent…
This paper deals with the problem of estimating a slope parameter in a simple linear regression model, where independent variables have functional measurement errors. Measurement errors in independent variables, as is well known, cause…
When working with quantum states, analysis of the final quantum state generated through probabilistic measurements is essential. This analysis is typically conducted by constructing the density matrix from either partial or full tomography…
Quantum search has emerged as one of the most promising fields in quantum computing. State-of-the-art quantum search algorithms enable the search for specific elements in a distribution by monotonically increasing the density of these…
Equations governing the nonlinear dynamics of complex systems are usually unknown and indirect methods are used to reconstruct their manifolds. In turn, they depend on embedding parameters requiring other methods and long temporal sequences…
This report presents an Expectation-Maximization (EM) algorithm for estimation of the maximum-likelihood parameter values of constrained multivariate autoregressive Gaussian state-space (MARSS) models. The MARSS model can be written:…
The computation of the ground state (i.e. the eigenvector related to the smallest eigenvalue) is an important task in the simulation of quantum many-body systems. As the dimension of the underlying vector space grows exponentially in the…
We study randomized sketching methods for approximately solving least-squares problem with a general convex constraint. The quality of a least-squares approximation can be assessed in different ways: either in terms of the value of the…
We study a multi-period convex quadratic optimization problem, where the state evolves dynamically as an affine function of the state, control, and indicator variables in each period. We begin by projecting out the state variables using…
High-dimensional matrix regression has been studied in various aspects, such as statistical properties, computational efficiency and application to specific instances including multivariate regression, system identification and matrix…
Regression analysis is an important instrument to determine the effect of the explanatory variables on response variables. When outliers and bias errors are present, the standard weighted least squares estimator may perform poorly. For this…
Structured distributions, i.e. distributions over combinatorial spaces, are commonly used to learn latent probabilistic representations from observed data. However, scaling these models is bottlenecked by the high computational and memory…
This article is an extended version of previous work of the authors [40, 41] on low-rank matrix estimation in the presence of constraints on the factors into which the matrix is factorized. Low-rank matrix factorization is one of the basic…