Machine learning suffers from a fundamental problem. While machines are able to learn complex prediction rules by minimizing their training error, data are often marred by selection biases, confounding factors, and other peculiarities [49,48,23]. As such, machines justifiably inherit these data biases. This limitation plays an essential role in the situations where machine learning fails to fulfill the promises of artificial intelligence. More specifically, minimizing training error leads machines into recklessly absorbing all the correlations found in training data. Understanding which patterns are useful has been previously studied as a correlation-versus-causation dilemma, since spurious correlations stemming from data biases are unrelated to the causal explanation of interest [31,27,35,52]. Following this line, we leverage tools from causation to develop the mathematics of spurious and invariant correlations, in order to alleviate the excessive reliance of machine learning systems on data biases, allowing them to generalize to new test distributions.As a thought experiment, consider the problem of classifying images of cows and camels [4]. To address this task, we label images of both types of animals. Due to a selection bias, most pictures of cows are taken in green pastures, while most pictures of camels happen to be in deserts. After training a convolutional neural network on this dataset, we observe that the model fails to classify easy examples of images of cows when they are taken on sandy beaches. Bewildered, we later realize that our neural network successfully minimized its training error using a simple cheat: classify green landscapes as cows, and beige landscapes as camels.To solve the problem described above, we need to identify which properties of the training data describe spurious correlations (landscapes and contexts), and which properties represent the phenomenon of interest (animal shapes). Intuitively, a correlation is spurious when we do not expect it to hold in the future in the same manner as it held in the past. In other words, spurious correlations do not appear to be stable properties [54]. Unfortunately, most datasets are not provided in a form amenable to discover stable properties. Because most machine learning algorithms depend on the assumption that training and testing data are sampled independently from the same distribution [51], it is common practice to shuffle at random the training and testing examples. For instance, whereas the original NIST handwritten data was collected from different writers under different conditions [19], the popular MNIST training and testing sets [8] were carefully shuffled to represent similar mixes of writers. Shuffling brings the training and testing distributions closer together, but

Generative Adversarial Networks (GANs) are powerful generative models, but suffer from training instability. The recently proposed Wasserstein GAN (WGAN) makes progress toward stable training of GANs, but sometimes can still generate only poor samples or fail to converge. We find that these problems are often due to the use of weight clipping in WGAN to enforce a Lipschitz constraint on the critic, which can lead to undesired behavior. We propose an alternative to clipping weights: penalize the norm of gradient of the critic with respect to its input. Our proposed method performs better than standard WGAN and enables stable training of a wide variety of GAN architectures with almost no hyperparameter tuning, including 101-layer ResNets and language models with continuous generators. We also achieve high quality generations on CIFAR-10 and LSUN bedrooms. † * Now at Google Brain † Code for our models is available at https://github.com/igul222/improved_wgan_training.

The goal of domain generalization algorithms is to predict well on distributions different from those seen during training. While a myriad of domain generalization algorithms exist, inconsistencies in experimental conditions-datasets, architectures, and model selection criteria-render fair and realistic comparisons difficult. In this paper, we are interested in understanding how useful domain generalization algorithms are in realistic settings. As a first step, we realize that model selection is non-trivial for domain generalization tasks. Contrary to prior work, we argue that domain generalization algorithms without a model selection strategy should be regarded as incomplete. Next, we implement DOMAINBED, a testbed for domain generalization including seven multi-domain datasets, nine baseline algorithms, and three model selection criteria. We conduct extensive experiments using DO-MAINBED and find that, when carefully implemented, empirical risk minimization shows state-of-the-art performance across all datasets. Looking forward, we hope that the release of DOMAINBED, along with contributions from fellow researchers, will streamline reproducible and rigorous research in domain generalization. * Alphabetical order, equal contribution.Preprint. Under review.

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