Deep networks have been successfully applied to learn transferable features for adapting models from a source domain to a different target domain. In this paper, we present joint adaptation networks (JAN), which learn a transfer network by aligning the joint distributions of multiple domain-specific layers across domains based on a joint maximum mean discrepancy (JMMD) criterion. Adversarial training strategy is adopted to maximize JMMD such that the distributions of the source and target domains are made more distinguishable. Learning can be performed by stochastic gradient descent with the gradients computed by back-propagation in linear-time. Experiments testify that our model yields state of the art results on standard datasets.
Let X denote the feature and Y the target. We consider domain adaptation under three possible scenarios: (1) the marginal PY changes, while the conditional PX Y stays the same (target shift), (2) the marginal PY is fixed, while the conditional PX Y changes with certain constraints (conditional shift), and (3) the marginal PY changes, and the conditional PX Y changes with constraints (generalized target shift). Using background knowledge, causal interpretations allow us to determine the correct situation for a problem at hand. We exploit importance reweighting or sample transformation to find the learning machine that works well on test data, and propose to estimate the weights or transformations by reweighting or transforming training data to reproduce the covariate distribution on the test domain. Thanks to kernel embedding of conditional as well as marginal distributions, the proposed approaches avoid distribution estimation, and are applicable for high-dimensional problems. Numerical evaluations on synthetic and real-world data sets demonstrate the effectiveness of the proposed framework. Transfer learning algorithms are used when one has sufficient training data for one supervised learning task (the source training domain) but only very limited training data for a second task (the target test domain) that is similar but not identical to the first. Previous work on transfer learning has focused on relatively restricted settings, where specific parts of the model are considered to be carried over between tasks. Recent work on covariate shift focuses on matching the marginal distributions on observations X across domains. Similarly, work on target conditional shift focuses on matching marginal distributions on labels Y and adjusting conditional distributions P(X|Y ), such that P(X) can be matched across domains. However, covariate shift assumes that the support of test P(X) is contained in the support of training P(X), i.e., the training set is richer than the test set. Target conditional shift makes a similar assumption for P(Y). Moreover, not much work on transfer learning has considered the case when a few labels in the test domain are available. Also little work has been done when all marginal and conditional distributions are allowed to change while the changes are smooth. In this paper, we consider a general case where both the support and the model change across domains. We transform both X and Y by a location-scale shift to achieve transfer between tasks. Since we allow more flexible transformations, the proposed method yields better results on both synthetic data and real-world data. Dataset shift is a common problem in predictive modeling that occurs when the joint distribution of inputs and outputs differs between training and test stages. Covariate shift, a particular case of dataset shift, occurs when only the input distribution changes. Dataset shift is present in most practical applications, for reasons ranging from the bias introduced by experimental design to the irreproducibility of the testing conditions at training time. (An example is -email spam filtering, which may fail to recognize spam that differs in form from the spam the automatic filter has been built on.) Despite this, and despite the attention given to the apparently similar problems of semi-supervised learning and active learning, dataset shift has received relatively little attention in the machine learning community until recently. This volume offers an overview of current efforts to deal with dataset and covariate shift. The chapters offer a mathematical and philosophical introduction to the problem, place dataset shift in relationship to transfer learning, transduction, local learning, active learning, and semi-supervised learning, provide theoretical views of dataset and covariate shift (including decision theoretic and Bayesian perspectives), and present algorithms for covariate shift. Contributors: Shai Ben-David, Steffen Bickel, Karsten Borgwardt, Michael Brckner, David Corfield, Amir Globerson, Arthur Gretton, Lars Kai Hansen, Matthias Hein, Jiayuan Huang, Takafumi Kanamori, Klaus-Robert Mller, Sam Roweis, Neil Rubens, Tobias Scheffer, Marcel Schmittfull, Bernhard Schlkopf, Hidetoshi Shimodaira, Alex Smola, Amos Storkey, Masashi Sugiyama, Choon Hui Teo Neural Information Processing series In this paper, we extend the Hilbert space embedding approach to handle conditional distributions. We derive a kernel estimate for the conditional embedding, and show its connection to ordinary embeddings. Conditional embeddings largely extend our ability to manipulate distributions in Hilbert spaces, and as an example, we derive a nonparametric method for modeling dynamical systems where the belief state of the system is maintained as a conditional embedding. Our method is very general in terms of both the domains and the types of distributions that it can handle, and we demonstrate the effectiveness of our method in various dynamical systems. We expect that conditional embeddings will have wider applications beyond modeling dynamical systems. A Hilbert space embedding for probability measures has recently been proposed, with applications including dimensionality reduction, homogeneity testing, and independence testing. This embedding represents any probability measure as a mean element in a reproducing kernel Hilbert space (RKHS). A pseudometric on the space of probability measures can be defined as the distance between distribution embeddings: we denote this as γk, indexed by the kernel function k that defines the inner product in the RKHS. We present three theoretical properties of γk. First, we consider the question of determining the conditions on the kernel k for which γk is a metric: such k are denoted characteristic kernels. Unlike pseudometrics, a metric is zero only when two distributions coincide, thus ensuring the RKHS embedding maps all distributions uniquely (i.e., the embedding is injective). While previously published conditions may apply only in restricted circumstances (e.g., on compact domains), and are difficult to check, our conditions are straightforward and intuitive: integrally strictly positive definite kernels are characteristic. Alternatively, if a bounded continuous kernel is translation-invariant on ℜd, then it is characteristic if and only if the support of its Fourier transform is the entire ℜd. Second, we show that the distance between distributions under γk results from an interplay between the properties of the kernel and the distributions, by demonstrating that distributions are close in the embedding space when their differences occur at higher frequencies. Third, to understand the nature of the topology induced by γk, we relate γk to other popular metrics on probability measures, and present conditions on the kernel k under which γk metrizes the weak topology. We consider the scenario where training and test data are drawn from different distributions, commonly referred to as sample selection bias. Most algorithms for this setting try to first recover sampling distributions and then make appropriate corrections based on the distribution estimate. We present a nonparametric method which directly produces resampling weights without distribution estimation. Our method works by matching distributions between training and testing sets in feature space. Experimental results demonstrate that our method works well in practice. A situation where training and test samples follow different input distributions is called covariate shift. Under covariate shift, standard learning methods such as maximum likelihood estimation are no longer consistent—weighted variants according to the ratio of test and training input densities are consistent. Therefore, accurately estimating the density ratio, called the importance, is one of the key issues in covariate shift adaptation. A naive approach to this task is to first estimate training and test input densities separately and then estimate the importance by taking the ratio of the estimated densities. However, this naive approach tends to perform poorly since density estimation is a hard task particularly in high dimensional cases. In this paper, we propose a direct importance estimation method that does not involve density estimation. Our method is equipped with a natural cross validation procedure and hence tuning parameters such as the kernel width can be objectively optimized. Simulations illustrate the usefulness of our approach. Hidden Markov Models (HMMs) are important tools for modeling sequence data. However, they are restricted to discrete latent states, and are largely restricted to Gaussian and discrete observations. And, learning algorithms for HMMs have predominantly relied on local search heuristics, with the exception of spectral methods such as those described below. We propose a nonparametric HMM that extends traditional HMMs to structured and non-Gaussian continuous distributions. Furthermore, we derive a local-minimum-free kernel spectral algorithm for learning these HMMs. We apply our method to robot vision data, slot car inertial sensor data and audio event classification data, and show that in these applications, embedded HMMs exceed the previous state-of-the-art performance.