Related papers: Generalized statistics: applications to data inver…
Bayesian posterior distributions arising in modern applications, including inverse problems in partial differential equation models in tomography and subsurface flow, are often computationally intractable due to the large computational cost…
Gauss' law of error is generalized in Tsallis statistics such as multifractal systems, in which Tsallis entropy plays an essential role instead of Shannon entropy. For the generalization, we apply the new multiplication operation determined…
The statistical inverse problem of estimating the probability distribution of an infinite-dimensional unknown given its noisy indirect observation is studied in the Bayesian framework. In practice, one often considers only…
We propose a generalized entropy maximization procedure, which takes into account the generalized averaging procedures and information gain definitions underlying the generalized entropies. This novel generalized procedure is then applied…
We present a likelihood-free probabilistic inversion method based on normalizing flows for high-dimensional inverse problems. The proposed method is composed of two complementary networks: a summary network for data compression and an…
We consider the problem of robustly fitting a model to data that includes outliers by formulating a percentile optimization problem. This problem is non-smooth and non-convex, hence hard to solve. We derive properties that the minimizers of…
This paper presents a unified geometric framework for the statistical analysis of a general ill-posed linear inverse model which includes as special cases noisy compressed sensing, sign vector recovery, trace regression, orthogonal matrix…
We study an inverse random obstacle scattering problems in $\mathbb{R}^2$ where the scatterer is formulated by a Gaussian process defined on the angular parameter domain. Equipped with a modified covariance function which is mathematically…
Many inverse problems include nuisance parameters which, while not of direct interest, are required to recover primary parameters. Structure present in these problems allows efficient optimization strategies - a well known example is…
Linear regression is ubiquitous in statistical analysis. It is well understood that conflicting sources of information may contaminate the inference when the classical normality of errors is assumed. The contamination caused by the light…
This paper focusses on robust estimation of location and concentration parameters of the von Mises-Fisher distribution in the Bayesian framework. The von Mises-Fisher (or Langevin) distribution has played a central role in directional…
Inverse problems are often ill-posed, with solutions that depend sensitively on data. In any numerical approach to the solution of such problems, regularization of some form is needed to counteract the resulting instability. This paper is…
This paper proposes an adaptive penalized weighted mean regression for outlier detection of high-dimensional data. In comparison to existing approaches based on the mean shift model, the proposed estimators demonstrate robustness against…
Inverse problems, where in broad sense the task is to learn from the noisy response about some unknown function, usually represented as the argument of some known functional form, has received wide attention in the general scientific…
Forecasting multivariate time series is a computationally intensive task challenged by extreme or redundant samples. Recent resampling methods aim to increase training efficiency by reweighting samples based on their running losses.…
Ordinal response model is a popular and commonly used regression for ordered categorical data in a wide range of fields such as medicine and social sciences. However, it is empirically known that the existence of ``outliers'', combinations…
Outliers are the points which are different from or inconsistent with the rest of the data. They can be novel, new, abnormal, unusual or noisy information. Outliers are sometimes more interesting than the majority of the data. The main…
A fundamental problem of statistical data analysis, distribution density estimation by experimental data, is considered. A new method with optimal asymptotic behavior, the root density estimator, is developed. The method proposed may be…
Inverse problems, i.e., estimating parameters of physical models from experimental data, are ubiquitous in science and engineering. The Bayesian formulation is the gold standard because it alleviates ill-posedness issues and quantifies…
We propose optimal dimensionality reduction techniques for the solution of goal-oriented linear-Gaussian inverse problems, where the quantity of interest (QoI) is a function of the inversion parameters. These approximations are suitable for…