Related papers: Using parameter elimination to solve discrete line…
We develop adaptive discretization algorithms for locally optimal experimental design of nonlinear prediction models. With these algorithms, we refine and improve a pertinent state-of-the-art algorithm in various respects. We establish…
Chance constrained program where one seeks to minimize an objective over decisions which satisfy randomly disturbed constraints with a given probability is computationally intractable. This paper proposes an approximate approach to address…
This paper investigates model reduction methods for efficiently approximating the solution of parameter-dependent PDEs with a multi-parameter vector $\vec{\mu} \in \mathbb{R}^p$. In cases where the Kolmogorov $N$-width decays fast enough,…
Overdetermined systems of first kind integral equations appear in many applications. When the right-hand side is discretized, the resulting finite-data problem is ill-posed and admits infinitely many solutions. We propose a numerical method…
Multi-material design optimization problems can, after discretization, be solved by the iterative solution of simpler sub-problems which approximate the original problem at an expansion point to first order. In particular, models…
A two-stage batch estimation algorithm for solving a class of nonlinear, static parameter estimation problems that appear in aerospace engineering applications is proposed. It is shown how these problems can be recast into a form suitable…
In this paper, a modification of the conventional approximations to the quasi-maximum likelihood method is introduced for the parameter estimation of diffusion processes from discrete observations. This is based on a convergent…
Modern large-scale statistical models require to estimate thousands to millions of parameters. This is often accomplished by iterative algorithms such as gradient descent, projected gradient descent or their accelerated versions. What are…
In this paper we design and analyze algorithms for asynchronously solving linear programs using nonlinear signal processing structures. In particular, we discuss a general procedure for generating these structures such that a fixed-point of…
Dimension reduction algorithms are a crucial part of many data science pipelines, including data exploration, feature creation and selection, and denoising. Despite their wide utilization, many non-linear dimension reduction algorithms are…
Linear discriminant analysis (LDA) is a classical method for dimensionality reduction, where discriminant vectors are sought to project data to a lower dimensional space for optimal separability of classes. Several recent papers have…
This paper studies deep neural networks for solving extremely large linear systems arising from highdimensional problems. Because of the curse of dimensionality, it is expensive to store both the solution and right-hand side vector in such…
Filtering and parameter estimation under partial information for multiscale problems is studied in this paper. After proving mean square convergence of the nonlinear filter to a filter of reduced dimension, we establish that the conditional…
We present an acceleration method for sequences of large-scale linear systems, such as the ones arising from the numerical solution of time-dependent partial differential equations coupled with algebraic constraints. We discuss different…
We present effective numerical algorithms for locally recovering unknown governing differential equations from measurement data. We employ a set of standard basis functions, e.g., polynomials, to approximate the governing equation with high…
Application of the minimum distance method to the linear regression model for estimating regression parameters is a difficult and time-consuming process due to the complexity of its distance function, and hence, it is computationally…
Multi-objective verification problems of parametric Markov decision processes under optimality criteria can be naturally expressed as nonlinear programs. We observe that many of these computationally demanding problems belong to the…
Robust parameter estimation is a crucial task in several 3D computer vision pipelines such as Structure from Motion (SfM). State-of-the-art algorithms for robust estimation, however, still suffer from difficulties in converging to…
Linear regression studies the problem of estimating a model parameter $\beta^* \in \mathbb{R}^p$, from $n$ observations $\{(y_i,\mathbf{x}_i)\}_{i=1}^n$ from linear model $y_i = \langle \mathbf{x}_i,\beta^* \rangle + \epsilon_i$. We…
We consider discrete optimization problems with interval uncertatinty of objective function coefficients. The interval uncertainty models measurements errors. A pos\-sible optimal solution is a solution that is optimal for some possible…