相关论文: A Note on Regularized Shannon's Sampling Formulae

The Reduced Basis (RB) method is a well established method for the model order reduction of problems formulated as parametrized partial differential equations. One crucial requirement for the application of RB schemes is the availability of…

Recent theoretical studies proved that deep neural network (DNN) estimators obtained by minimizing empirical risk with a certain sparsity constraint can attain optimal convergence rates for regression and classification problems. However,…

We introduce unbiased estimators for the Shannon entropy and the class number, in the situation that we are able to take sequences of independent samples of arbitrary length.

We give an efficient algorithm which can obtain a relative error approximation to the spectral norm of a matrix, combining the power iteration method with some techniques from matrix reconstruction which use random sampling.

A new sampling methodology based on incomplete cosine expansion series is presented as an alternative to the traditional sinc function approach. Numerical integration shows that this methodology is efficient and practical. Applying the…

We establish sharp geometric $C^{1+\alpha}$ regularity estimates for bounded weak solutions of evolution equations of $p$-Laplacian type. Our approach is based on geometric tangential methods, and makes use of a systematic oscillation…

This paper presents a general framework for estimating high-dimensional conditional latent factor models via constrained nuclear norm regularization. We establish large sample properties of the estimators and provide efficient algorithms…

The average properties of the well-known Subset Sum Problem can be studied by the means of its randomised version, where we are given a target value $z$, random variables $X_1, \ldots, X_n$, and an error parameter $\varepsilon > 0$, and we…

We present a general framework for studying regularized estimators; such estimators are pervasive in estimation problems wherein "plug-in" type estimators are either ill-defined or ill-behaved. Within this framework, we derive, under…

Science and engineering problems subject to uncertainty are frequently both computationally expensive and feature nonsmooth parameter dependence, making standard Monte Carlo too slow, and excluding efficient use of accelerated uncertainty…

This paper develops a probabilistic numerical method for solution of partial differential equations (PDEs) and studies application of that method to PDE-constrained inverse problems. This approach enables the solution of challenging inverse…

Calculating the Shannon entropy for symbolic sequences has been widely considered in many fields. For descriptive statistical problems such as estimating the N-gram entropy of English language text, a common approach is to use as much data…

Importance sampling is a popular method for efficient computation of various properties of a distribution such as probabilities, expectations, quantiles etc. The output of an importance sampling algorithm can be represented as a weighted…

We discuss perturbative solutions of renormalization group equations, and propose the use of resummation scale techniques in assessing theoretical uncertainties on the extraction of parton distribution functions from data.

This paper describes a new comparison principle that can be used for the comparison of space-time estimates for dispersive equations. In particular, results are applied to the global smoothing estimates for several classes of dispersive…

A main drawback of classical Tikhonov regularization is that often the parameters required to apply theoretical results, e.g., the smoothness of the sought-after solution and the noise level, are unknown in practice. In this paper we…

Estimating the uncertainty in deep neural network predictions is crucial for many real-world applications. A common approach to model uncertainty is to choose a parametric distribution and fit the data to it using maximum likelihood…

Surveys usually suffer from non-response, which decreases the effective sample size. Item non-response is typically handled by means of some form of random imputation if we wish to preserve the distribution of the imputed variable. This…

Regularization plays an important role in solving ill-posed problems by adding extra information about the desired solution, such as sparsity. Many regularization terms usually involve some vector norm, e.g., $L_1$ and $L_2$ norms. In this…

Statistical applications often involve the calculation of intractable multidimensional integrals. The Laplace formula is widely used to approximate such integrals. However, in high-dimensional or small sample size problems, the shape of the…