Related papers: Regularization of statistical inverse problems and…

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…

We formulate a principle for classification with the knowledge of the marginal distribution over the data points (unlabeled data). The principle is cast in terms of Tikhonov style regularization where the regularization penalty articulates…

We provide a necessary and sufficient condition for a rough control driving a differential equation to be reconstructable, to some order, from observing the resulting controlled evolution. Physical examples and applications in stochastic…

In this paper we elaborate on the recently proposed superstatistics formalism [C. Beck and E.G.D. Cohen, Physica A 322, 267 (2003)], used to interpret unconventional statistics. Their interpretation is that unconventional statistics in…

We develop a data-driven algorithm for automatically selecting the regularisation parameter in Bayesian inversion under random tree Besov priors. One of the key challenges in Bayesian inversion is the construction of priors that are both…

Though learning has become a core component of modern information processing, there is now ample evidence that it can lead to biased, unsafe, and prejudiced systems. The need to impose requirements on learning is therefore paramount,…

We consider a control-constrained parabolic optimal control problem without Tikhonov term in the tracking functional. For the numerical treatment, we use variational discretization of its Tikhonov regularization: For the state and the…

In this work, we investigate the regularized solutions and their finite element solutions to the inverse source problems governed by partial differential equations, and establish the stochastic convergence and optimal finite element…

Many learning machines such as normal mixtures and layered neural networks are not regular but singular statistical models, because the map from a parameter to a probability distribution is not one-to-one. The conventional statistical…

Time reversal symmetry is a fundamental property of many quantum mechanical systems. The relation between statistical physics and time reversal is subtle and not all statistical theories conserve this particular symmetry, most notably…

In this article we investigate the connection between regularization theory for inverse problems and dynamic programming theory. This is done by developing two new regularization methods, based on dynamic programming techniques. The aim of…

Regular variation of distributional tails is known to be preserved by various linear transformations of some random structures. An inverse problem for regular variation aims at understanding whether the regular variation of a transformed…

Regularization is a central tool for addressing ill-posedness in inverse problems and statistical estimation, with the choice of a suitable penalty often determining the reliability and interpretability of downstream solutions. While recent…

We study the problem of regularization of inverse problems adopting a purely data driven approach, by using the similarity to the method of regularization by projection. We provide an application of a projection algorithm, utilized and…

We study the inverse problem of deducing the dynamical characteristics (such as the potential field) of large systems from kinematic observations. We show that, for a class of steady-state systems, the solution is unique even with…

Although the \emph{residual method}, or \emph{constrained regularization}, is frequently used in applications, a detailed study of its properties is still missing. This sharply contrasts the progress of the theory of Tikhonov…

Through extended consideration of two wide classes of case studies -- dilute gases and linear systems -- I explore the ways in which assumptions of probability and irreversibility occur in contemporary statistical mechanics, where the…

Database theory and database practice are typically the domain of computer scientists who adopt what may be termed an algorithmic perspective on their data. This perspective is very different than the more statistical perspective adopted by…

We propose a novel method for modeling data by using structural models based on economic theory as regularizers for statistical models. We show that even if a structural model is misspecified, as long as it is informative about the…

In inverse problems, it is widely recognized that the incorporation of a sparsity prior yields a regularization effect on the solution. This approach is grounded on the a priori assumption that the unknown can be appropriately represented…