Many works have shown that strong connections relate learning from examples to regularization techniques for ill-posed inverse problems. Nevertheless by now there was no formal evidence neither that learning from examples could be seen as an inverse problem nor that theoretical results in learning theory could be independently derived using tools from regularization theory. In this paper we pro...

the determination of an unknown boundary condition, in a nonlinaer inverse diffusion problem is considered. for solving these ill-posed inverse problems, galerkin method based on sinc basis functions for space and time will be used. to solve the system of linear equation, a noise is imposed and tikhonove regularization is applied. by using a sensor located at a point in the domain of $x$, say $...

In the Bayesian approach to ill-posed inverse problems, regularization is imposed by specifying a prior distribution on the parameters of interest and Markov chain Monte Carlo samplers are used to extract information about its posterior distribution. The aim of this paper is to investigate the convergence properties of the random-scan random-walk Metropolis (RSM) algorithm for posterior distrib...

A parameter of an econometric model is identified if there is a one-to-one or many-to-one mapping from the population distribution of the available data to the parameter. Often, this mapping is obtained by inverting a mapping from the parameter to the population distribution. If the inverse mapping is discontinuous, then estimation of the parameter usually presents an illposed inverse problem. ...