Related papers: An Additive Approximation to Multiplicative Noise
Implicit sampling is a weighted sampling method that is used in data assimilation, where one sequentially updates estimates of the state of a stochastic model based on a stream of noisy or incomplete data. Here we describe how to use…
Composite likelihood provides approximate inference when the full likelihood is intractable and sub-likelihood functions of marginal events can be evaluated relatively easily. It has been successfully applied for many complex models.…
This purpose of this paper is to locate a single localized source from three range measurements with multiplicative noises. Although some minimization approaches for additive noise have been found, studies on the existence of solutions are…
By exploiting the well-known observation that size-biasing or zero-biasing an infinitely divisible random variable may be achieved by adding an independent increment, combined with tools from Stein's method for compound Poisson and Gaussian…
In this paper we consider from two different aspects the proximal alternating direction method of multipliers (ADMM) in Hilbert spaces. We first consider the application of the proximal ADMM to solve well-posed linearly constrained…
Unsupervised Anomalous Sound Detection (ASD) aims to design a generalizable method that can be used to detect anomalies when only normal sounds are given. In this paper, Anomalous Sound Detection based on Diffusion Models (ASD-Diffusion) is…
The purpose of this note is to show how the method of maximum entropy in the mean (MEM) may be used to improve parametric estimation when the measurements are corrupted by large level of noise. The method is developed in the context on a…
For many optimization problems it is possible to define a distance metric between problem variables that correlates with the likelihood and strength of interactions between the variables. For example, one may define a metric so that the…
The recent statistical theory of neural networks focuses on nonparametric denoising problems that treat randomness as additive noise. Variability in image classification datasets does, however, not originate from additive noise but from…
Regularization is a common tool in variational inverse problems to impose assumptions on the parameters of the problem. One such assumption is sparsity, which is commonly promoted using lasso and total variation-like regularization.…
The marginal likelihood is a well established model selection criterion in Bayesian statistics. It also allows to efficiently calculate the marginal posterior model probabilities that can be used for Bayesian model averaging of quantities…
Many imaging problems require solving an inverse problem that is ill-conditioned or ill-posed. Imaging methods typically address this difficulty by regularising the estimation problem to make it well-posed. This often requires setting the…
The emergent field of probabilistic numerics has thus far lacked clear statistical principals. This paper establishes Bayesian probabilistic numerical methods as those which can be cast as solutions to certain inverse problems within the…
Measurements are a vital part of any quantum computation, whether as a final step to retrieve results, as an intermediate step to inform subsequent operations, or as part of the computation itself (as in measurement-based quantum…
In this paper, we study the sparse nonnegative tensor factorization and completion problem from partial and noisy observations for third-order tensors. Because of sparsity and nonnegativity, the underlying tensor is decomposed into the…
This work is focussed on the inversion task of inferring the distribution over parameters of interest leading to multiple sets of observations. The potential to solve such distributional inversion problems is driven by increasing…
Gaussian mixtures are a common density representation in nonlinear, non-Gaussian Bayesian state estimation. Selecting an appropriate number of Gaussian components, however, is difficult as one has to trade of computational complexity…
In computational mechanics, multiple models are often present to describe a physical system. While Bayesian model selection is a helpful tool to compare these models using measurement data, it requires the computationally expensive…
Deconvolution is a statistical inverse problem to estimate the distribution of a random variable based on its noisy observations. Despite the extensive studies on the topic, deconvolution with unknown noise distribution remains as a…
Masking methods for the safe dissemination of microdata consist of distorting the original data while preserving a pre-defined set of statistical properties in the microdata. For continuous variables, available methodologies rely…