Related papers: Approximation of Lyapunov Functions from Noisy Dat…
We present a Fourier-based approach for high-dimensional function approximation. To this end, we analyze the truncated ANOVA (analysis of variance) decomposition and learn the anisotropic smoothness properties of the target function from…
Covariant Lyapunov vectors characterize the directions along which perturbations in dynamical systems grow. They have also been studied as predictors of critical transitions and extreme events. For many applications like, for example,…
Because of the high approximation power and simplicity of computation of smooth radial basis functions (RBFs), in recent decades they have received much attention for function approximation. These RBFs contain a shape parameter that…
We study fast approximation of integrals with respect to stationary probability measures associated to iterated functions systems on the unit interval. We provide an algorithm for approximating the integrals under certain conditions on the…
This article addresses the challenge of learning effective regularizers for linear inverse problems. We analyze and compare several types of learned variational regularization against the theoretical benchmark of the optimal affine…
In this paper, we propose two algorithms for solving linear inverse problems when the observations are corrupted by Poisson noise. A proper data fidelity term (log-likelihood) is introduced to reflect the Poisson statistics of the noise. On…
We propose an alternative to $k$-nearest neighbors for functional data whereby the approximating neighboring curves are piecewise functions built from a functional sample. Using a locally defined distance function that satisfies…
Recent advances in deep learning have relied on large, labelled datasets to train high-capacity models. However, collecting large datasets in a time- and cost-efficient manner often results in label noise. We present a method for learning…
We propose CoNSAL (Combining Neural networks and Symbolic regression for Analytical Lyapunov function) to construct analytical Lyapunov functions for nonlinear dynamic systems. This framework contains a neural Lyapunov function and a…
This paper presents a proof that existence of a polynomial Lyapunov function is necessary and sufficient for exponential stability of sufficiently smooth nonlinear ordinary differential equations on bounded sets. The main result states that…
We derive a method to reconstruct Gaussian signals from linear measurements with Gaussian noise. This new algorithm is intended for applications in astrophysics and other sciences. The starting point of our considerations is the principle…
Despite their spectacular progress, language models still struggle on complex reasoning tasks, such as advanced mathematics. We consider a long-standing open problem in mathematics: discovering a Lyapunov function that ensures the global…
Approximating functions by a linear span of truncated basis sets is a standard procedure for the numerical solution of differential and integral equations. Commonly used concepts of approximation methods are well-posed and convergent, by…
In this paper, we propose an iterative method for using SOS programming to estimate the region of attraction of a polynomial vector field, the conjectured convergence of which necessitates the existence of polynomial Lyapunov functions…
Bayesian techniques are widely used to obtain spectral functions from correlators. We suggest a technique to rid the results of nuisance parameters, ie, parameters which are needed for the regularization but cannot be determined from data.…
We propose a general algorithm for approximating nonstandard Bayesian posterior distributions. The algorithm minimizes the Kullback-Leibler divergence of an approximating distribution to the intractable posterior distribution. Our method…
We recently proposed a general algorithm for approximating nonstandard Bayesian posterior distributions by minimization of their Kullback-Leibler divergence with respect to a more convenient approximating distribution. In this note we offer…
Trigonometric polynomials are widely used for the approximation of a smooth function $f$ from a set of nonuniformly spaced samples $\{f(x_j)\}_{j=0}^{N-1}$. If the samples are perturbed by noise, controlling the smoothness of the…
Submodular function minimization is well studied, and existing algorithms solve it exactly or up to arbitrary accuracy. However, in many applications, such as structured sparse learning or batch Bayesian optimization, the objective function…
This paper addresses the gradient flow -- the continuous-time representation of the gradient method -- with the smooth approximation of a non-differentiable objective function and presents convergence analysis framework. Similar to the…