Related papers: Sampling in BV-Type Spaces
Estimation of mean and covariance functions is fundamental for functional data analysis. While this topic has been studied extensively in the literature, a key assumption is that there are enough data in the domain of interest to estimate…
The translation of an operator is defined by using conjugation with time-frequency shifts. Thus, one can define $\Lambda$-shift-invariant subspaces of Hilbert-Schmidt operators, finitely generated, with respect to a lattice $\Lambda$ in…
We study a novel class of affine invariant and consistent tests for normality in any dimension. The tests are based on a characterization of the standard $d$-variate normal distribution as the unique solution of an initial value problem of…
Deep neural networks, when optimized with sufficient data, provide accurate representations of high-dimensional functions; in contrast, function approximation techniques that have predominated in scientific computing do not scale well with…
We consider approximation or recovery of functions based on a finite number of function evaluations. This is a well-studied problem in optimal recovery, machine learning, and numerical analysis in general, but many fundamental insights were…
Diffusion models have emerged as powerful learned priors for Bayesian inverse problems (BIPs). Diffusion-based solvers rely on a presumed likelihood for the observations in BIPs to guide the generation process. Likelihood misspecification…
We extend some results about sampling of entire functions of exponential type to Banach spaces. By using generator $D$ of one-parameter group $e^{tD}$ of isometries of a Banach space $E$ we introduce Bernstein subspaces…
We first describe a general class of optimization problems that describe many natural, economic, and statistical phenomena. After noting the existence of a conserved quantity in a transformed coordinate system, we outline several instances…
This paper addresses the issue of inversion in cases where (1) the observation system is modeled by a linear transformation and additive noise, (2) the problem is ill-posed and regularization is introduced in a Bayesian framework by an a…
Bayesian optimisation is a powerful tool to solve expensive black-box problems, but fails when the stationary assumption made on the objective function is strongly violated, which is the case in particular for ill-conditioned or…
Deep learning requires regularization mechanisms to reduce overfitting and improve generalization. We address this problem by a new regularization method based on distributional robust optimization. The key idea is to modify the…
This paper is concerned with a novel regularisation technique for solving linear ill-posed operator equations in Hilbert spaces from data that is corrupted by white noise. We combine convex penalty functionals with extreme-value statistics…
Sampling and reconstruction of functions is a central tool in science. A key result is given by the sampling theorem for bandlimited functions attributed to Whittaker, Shannon, Nyquist, and Kotelnikov. We develop an analogous sampling…
Recently the characterization of the compactness in the space $BV([0,1])$ of functions of bounded Jordan variation was given. Here, certain generalizations of this result are given for the spaces of functions of bounded Waterman…
Monte Carlo methods, Variational Inference, and their combinations play a pivotal role in sampling from intractable probability distributions. However, current studies lack a unified evaluation framework, relying on disparate performance…
Bayesian optimization has proven to be a highly effective methodology for the global optimization of unknown, expensive and multimodal functions. The ability to accurately model distributions over functions is critical to the effectiveness…
We present an extension of local sensitivity analysis, also referred to as the perturbation approach for uncertainty quantification, to Bayesian inverse problems. More precisely, we show how moments of random variables with respect to the…
The continuous variable quantum computing platform constitutes a promising candidate for realizing quantum advantage, as exemplified in Gaussian Boson Sampling. While noise in the experiments makes the computation attainable for classical…
Let $B^p_{\sigma}$, $1\le p<\infty$, $\sigma>0$, denote the space of all $f\in L^p(\mathbb{R})$ such that the Fourier transform of $f$ (in the sense of distributions) vanishes outside $[-\sigma,\sigma]$. The classical sampling theorem…
In this paper, we introduce a definition of BV functions in a Gelfand triple which is an extension of the definition of BV functions in [2] by using Dirichlet form theory. By this definition, we can consider the stochastic reflection…