Generalization Bounds for Representative Domain Adaptation

In this paper, we propose a novel framework to analyze the theoretical properties of the learning process for a representative type of domain adaptation, which combines data from multiple sources and one target (or briefly called representative domain adaptation). In particular, we use the integral probability metric to measure the difference between the distributions of two domains and meanwhile compare it with the H-divergence and the discrepancy distance. We develop the Hoeffding-type, the Bennett-type and the McDiarmid-type deviation inequalities for multiple domains respectively, and then present the symmetrization inequality for representative domain adaptation. Next, we use the derived inequalities to obtain the Hoeffding-type and the Bennett-type generalization bounds respectively, both of which are based on the uniform entropy number. Moreover, we present the generalization bounds based on the Rademacher complexity. Finally, we analyze the asymptotic convergence and the rate of convergence of the learning process for representative domain adaptation. We discuss the factors that affect the asymptotic behavior of the learning process and the numerical experiments support our theoretical findings as well. Meanwhile, we give a comparison with the existing results of domain adaptation and the classical results under the same-distribution assumption.Comment: arXiv admin note: substantial text overlap with arXiv:1304.157

Distribution-Based Categorization of Classifier Transfer Learning

Transfer Learning (TL) aims to transfer knowledge acquired in one problem, the source problem, onto another problem, the target problem, dispensing with the bottom-up construction of the target model. Due to its relevance, TL has gained significant interest in the Machine Learning community since it paves the way to devise intelligent learning models that can easily be tailored to many different applications. As it is natural in a fast evolving area, a wide variety of TL methods, settings and nomenclature have been proposed so far. However, a wide range of works have been reporting different names for the same concepts. This concept and terminology mixture contribute however to obscure the TL field, hindering its proper consideration. In this paper we present a review of the literature on the majority of classification TL methods, and also a distribution-based categorization of TL with a common nomenclature suitable to classification problems. Under this perspective three main TL categories are presented, discussed and illustrated with examples

Bounded-Distortion Metric Learning

Metric learning aims to embed one metric space into another to benefit tasks like classification and clustering. Although a greatly distorted metric space has a high degree of freedom to fit training data, it is prone to overfitting and numerical inaccuracy. This paper presents {\it bounded-distortion metric learning} (BDML), a new metric learning framework which amounts to finding an optimal Mahalanobis metric space with a bounded-distortion constraint. An efficient solver based on the multiplicative weights update method is proposed. Moreover, we generalize BDML to pseudo-metric learning and devise the semidefinite relaxation and a randomized algorithm to approximately solve it. We further provide theoretical analysis to show that distortion is a key ingredient for stability and generalization ability of our BDML algorithm. Extensive experiments on several benchmark datasets yield promising results