The ability to build a model on a source task and subsequently adapt such model on a new target task is a pervasive need in many astronomical applications. The problem is generally known as transfer learning in machine learning, where domain adaptation is a popular scenario. An example is to build a predictive model on spectroscopic data to identify Supernovae IA, while subsequently trying to adapt such model on photometric data. In this paper we propose a new general approach to domain adaptation that does not rely on the proximity of source and target distributions. Instead we simply assume a strong similarity in model complexity across domains, and use active learning to mitigate the dependency on source examples. Our work leads to a new formulation for the likelihood as a function of empirical error using a theoretical learning bound; the result is a novel mapping from generalization error to a likelihood estimation. Results using two real astronomical problems, Supernova Ia classification and identification of Mars landforms, show two main advantages with our approach: increased accuracy performance and substantial savings in computational cost.
From a theoretical view, previous work has tried to estimate the distance between source and target distributions @cite_5 @cite_2 @cite_8 ; and employ regularization terms to find models with good generalization performance on both source and target domains @cite_55 .
@cite_5 @cite_55 @cite_8 @cite_2
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This paper presents a theoretical analysis of the problem of domain adaptation with multiple sources. For each source domain, the distribution over the input points as well as a hypothesis with error at most ∊ are given. The problem consists of combining these hypotheses to derive a hypothesis with small error with respect to the target domain. We present several theoretical results relating to this problem. In particular, we prove that standard convex combinations of the source hypotheses may in fact perform very poorly and that, instead, combinations weighted by the source distributions benefit from favorable theoretical guarantees. Our main result shows that, remarkably, for any fixed target function, there exists a distribution weighted combining rule that has a loss of at most ∊ with respect to any target mixture of the source distributions. We further generalize the setting from a single target function to multiple consistent target functions and show the existence of a combining rule with error at most 3∊. Finally, we report empirical results for a multiple source adaptation problem with a real-world dataset. 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. The classic Generative Adversarial Net and its variants can be roughly categorized into two large families: the unregularized versus regularized GANs. By relaxing the non-parametric assumption on the discriminator in the classic GAN, the regularized GANs have better generalization ability to produce new samples drawn from the real distribution. It is well known that the real data like natural images are not uniformly distributed over the whole data space. Instead, they are often restricted to a low-dimensional manifold of the ambient space. Such a manifold assumption suggests the distance over the manifold should be a better measure to characterize the distinct between real and fake samples. Thus, we define a pullback operator to map samples back to their data manifold, and a manifold margin is defined as the distance between the pullback representations to distinguish between real and fake samples and learn the optimal generators. We justify the effectiveness of the proposed model both theoretically and empirically. 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 new 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 several algorithms. We report the results of preliminary experiments that demonstrate the benefits of our discrepancy minimization algorithms for domain adaptation.