Considerable e ort has been directed recently to develop asymptotically minimax methods in problems of recovering in nite-dimensional objects (curves, densities, spectral densities, images) from noisy data. A rich and complex body of work has evolved, with nearlyor exactlyminimax estimators being obtained for a variety of interesting problems. Unfortunately, the results have often not been tran...

In this paper we derive the bounds for Validation (known also as Hold-Out Estimate and Train-and-Test Method). We present the best possible bound in the case of 0-1 valued loss function. We also provide the tables where the least sample size is calculated that is necessary for obtaining the bound for a given estimation rate and reliability of estimation. For an arbitrary bounded loss function w...

This paper revisits the problem of learning a k-CNF Boolean function from examples, for fixed k, in the context of online learning under the logarithmic loss. We give a Bayesian interpretation to one of Valiant’s classic PAC learning algorithms, which we then build upon to derive three efficient, online, probabilistic, supervised learning algorithms for predicting the output of an unknown k-CNF...

Innovative multi-channel synthetic aperture radar (SAR) concepts enable high-resolution wide-swath imaging, but the antenna length typically restricts the achievable swath width. This limitation can be overcome by a novel technique which is based on a single azimuth channel but operates the system with a continuously varied pulse repetition frequency (PRF) by this allowing in principle for arbi...

Using differentiability assumptions on the loss function and a concentration inequality for bounded second order differences it is shown that the generalization error for classification with L2 regularisation obeys a Bernstein-type inequality.

‎let $x$ be a real normed  space, then  $c(subseteq x)$  is  functionally  convex  (briefly, $f$-convex), if  $t(c)subseteq bbb r $ is  convex for all bounded linear transformations $tin b(x,r)$; and $k(subseteq x)$  is  functionally   closed (briefly, $f$-closed), if  $t(k)subseteq bbb r $ is  closed  for all bounded linear transformations $tin b(x,r)$. we improve the    krein-milman theorem  ...

in zero acceptance number sampling plans, the sample items of an incoming lot are inspected one by one. the proposed method in this research follows these rules: if the number of nonconforming items in the first sample is equal to zero, the lot is accepted but if the number of nonconforming items is equal to one, then second sample is taken and the policy of zero acceptance number would be appl...

in this paper, a bayesian approach is proposed for shift point detection in an inverse gaussian distribution. in this study, the mean parameter of inverse gaussian distribution is assumed to be constant and shift points in shape parameter is considered. first the posterior distribution of shape parameter is obtained. then the bayes estimators are derived under a class of priors and using variou...