This work is motivated by the problem of image mis-registration in remote sensing and we are interested in determining the resulting loss in the accuracy of pattern classification. A statistical formulation is given where we propose to use data contamination to model and understand the phenomenon of image mis-registration. This model is widely applicable to many other types of errors as well, for example, measurement errors and gross errors etc. The impact of data contamination on classification is studied under a statistical learning theoretical framework. A closed-form asymptotic bound is established for the resulting loss in classification accuracy, which is less than @math for data contamination of an amount of @math . Our bound is sharper than similar bounds in the domain adaptation literature and, unlike such bounds, it applies to classifiers with an infinite Vapnik-Chervonekis (VC) dimension. Extensive simulations have been conducted on both synthetic and real datasets under various types of data contamination, including label flipping, feature swapping and the replacement of feature values with data generated from a random source such as a Gaussian or Cauchy distribution. Our simulation results show that the bound we derive is fairly tight.
This paper addresses the general problem of domain adaptation which arises in a variety of applications where the distribution of the labeled sample available somewhat differs from that of the test data. Building on previous work by Ben- (2007), we introduce a novel distance between distributions, discrepancy distance, that is tailored to adaptation problems with arbitrary loss functions. We give Rademacher complexity bounds for estimating the discrepancy distance from finite samples for different loss functions. Using this distance, we derive novel generalization bounds for domain adaptation for a wide family of loss functions. We also present a series of novel adaptation bounds for large classes of regularization-based algorithms, including support vector machines and kernel ridge regression based on the empirical discrepancy. This motivates our analysis of the problem of minimizing the empirical discrepancy for various loss functions for which we also give novel algorithms. We report the results of preliminary experiments that demonstrate the benefits of our discrepancy minimization algorithms for domain adaptation.  We investigate the use of certain data-dependent estimates of the complexity of a function class, called Rademacher and gaussian complexities. In a decision theoretic setting, we prove general risk bounds in terms of these complexities. We consider function classes that can be expressed as combinations of functions from basis classes and show how the Rademacher and gaussian complexities of such a function class can be bounded in terms of the complexity of the basis classes.We give examples of the application of these techniques in finding data-dependent risk bounds for decision trees, neural networks and support vector machines.