The learning of domain-invariant representations in the context of domain adaptation with neural networks is considered. We propose a new regularization method that minimizes the discrepancy between domain-specific latent feature representations directly in the hidden activation space. Although some standard distribution matching approaches exist that can be interpreted as the matching of weighted sums of moments, e.g. Maximum Mean Discrepancy (MMD), an explicit order-wise matching of higher order moments has not been considered before. We propose to match the higher order central moments of probability distributions by means of order-wise moment differences. Our model does not require computationally expensive distance and kernel matrix computations. We utilize the equivalent representation of probability distributions by moment sequences to define a new distance function, called Central Moment Discrepancy (CMD). We prove that CMD is a metric on the set of probability distributions on a compact interval. We further prove that convergence of probability distributions on compact intervals w.r.t. the new metric implies convergence in distribution of the respective random variables. We test our approach on two different benchmark data sets for object recognition (Office) and sentiment analysis of product reviews (Amazon reviews). CMD achieves a new state-of-the-art performance on most domain adaptation tasks of Office and outperforms networks trained with MMD, Variational Fair Autoencoders and Domain Adversarial Neural Networks on Amazon reviews. In addition, a post-hoc parameter sensitivity analysis shows that the new approach is stable w.r.t. parameter changes in a certain interval. The source code of the experiments is publicly available.
The two approaches MMD and the Proxy @math - distance have in common that they do not minimize the domain discrepancy explicitly in the hidden activation space. In contrast, the authors in @cite_5 do so by minimizing a modified version of the Kullback-Leibler divergence of the mean activations (MKL). That is, for samples @math , with @math being the @math coordinate of the empirical expectation @math . This approach is fast to compute and has an explicit interpretation in the activation space. Our empirical observations (section Experiments ) show that minimizing the distance between only the first moment (mean) of the activation distributions can be improved by also minimizing the distance between higher order moments.
@cite_5
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Transfer learning has attracted a lot of attention in the past decade. One crucial research issue in transfer learning is how to find a good representation for instances of different domains such that the divergence between domains can be reduced with the new representation. Recently, deep learning has been proposed to learn more robust or higherlevel features for transfer learning. However, to the best of our knowledge, most of the previous approaches neither minimize the difference between domains explicitly nor encode label information in learning the representation. In this paper, we propose a supervised representation learning method based on deep autoencoders for transfer learning. The proposed deep autoencoder consists of two encoding layers: an embedding layer and a label encoding layer. In the embedding layer, the distance in distributions of the embedded instances between the source and target domains is minimized in terms of KL-Divergence. In the label encoding layer, label information of the source domain is encoded using a softmax regression model. Extensive experiments conducted on three real-world image datasets demonstrate the effectiveness of our proposed method compared with several state-of-the-art baseline methods.