Related papers: Low Rank Approximation for Smoothing Spline via Ei…
Large-scale eigenvalue problems arise in various fields of science and engineering and demand computationally efficient solutions. In this study, we investigate the subspace approximation for parametric linear eigenvalue problems, aiming to…
In this paper, we develop approximation error estimates as well as corresponding inverse inequalities for B-splines of maximum smoothness, where both the function to be approximated and the approximation error are measured in standard…
The analysis of high-dimensional dynamical systems generally requires the integration of simulation data with experimental measurements. Experimental data often has substantial amounts of measurement noise that compromises the ability to…
This paper considers approximate smoothing for discretely observed non-linear stochastic differential equations. The problem is tackled by developing methods for linearising stochastic differential equations with respect to an arbitrary…
We propose a stochastic approximation method for approximating the efficient frontier of chance-constrained nonlinear programs. Our approach is based on a bi-objective viewpoint of chance-constrained programs that seeks solutions on the…
Low-rank approximation in data streams is a fundamental and significant task in computing science, machine learning and statistics. Multiple streaming algorithms have emerged over years and most of them are inspired by randomized…
The simulation of large nonlinear dynamical systems, including systems generated by discretization of hyperbolic partial differential equations, can be computationally demanding. Such systems are important in both fluid and kinetic…
In this paper, we explore statistical versus computational trade-off to address a basic question in the application of a distributed algorithm: what is the minimal computational cost in obtaining statistical optimality? In smoothing spline…
We consider the weighted least squares spline approximation of a noisy dataset. By interpreting the weights as a probability distribution, we maximize the associated entropy subject to the constraint that the mean squared error is…
This paper introduces a smoothed proximal Lagrangian method for minimizing a nonconvex smooth function over a convex domain with additional explicit convex nonlinear constraints. Two key features are 1) the proposed method is single-looped,…
Maximum likelihood (ML) estimation using Newton's method in nonlinear state space models (SSMs) is a challenging problem due to the analytical intractability of the log-likelihood and its gradient and Hessian. We estimate the gradient and…
The smoothing spline is one of the most popular curve-fitting methods, partly because of empirical evidence supporting its effectiveness and partly because of its elegant mathematical formulation. However, there are two obstacles that…
Sparse polynomial approximation has become indispensable for approximating smooth, high- or infinite-dimensional functions from limited samples. This is a key task in computational science and engineering, e.g., surrogate modelling in…
The low-complexity assumption in linear systems can often be expressed as rank deficiency in data matrices with generalized Hankel structure. This makes it possible to denoise the data by estimating the underlying structured low-rank…
Many applications in machine learning or signal processing involve nonsmooth optimization problems. This nonsmoothness brings a low-dimensional structure to the optimal solutions. In this paper, we propose a randomized proximal gradient…
Spatial modelling often uses Gaussian random fields to capture the stochastic nature of studied phenomena. However, this approach incurs significant computational burdens (O(n3)), primarily due to covariance matrix computations. In this…
The growing prevalence of nonsmooth optimization problems in machine learning has spurred significant interest in generalized smoothness assumptions. Among these, the (L0, L1)-smoothness assumption has emerged as one of the most prominent.…
In this work, we propose a new randomized algorithm for computing a low-rank approximation to a given matrix. Taking an approach different from existing literature, our method first involves a specific biased sampling, with an element being…
The Kalman filter and Rauch-Tung-Striebel (RTS) smoother are optimal for state estimation in linear dynamic systems. With nonlinear systems, the challenge consists in how to propagate uncertainty through the state transitions and output…
In this paper, we propose a low-rank approximation method based on discrete least-squares for the approximation of a multivariate function from random, noisy-free observations. Sparsity inducing regularization techniques are used within…