Domain generalization (DG) aims to learn from multiple source domains a model that can generalize well on unseen target domains. Existing DG methods mainly learn the representations with invariant marginal distribution of the input features, however, the invariance of the conditional distribution of the labels given the input features is more essential for unknown domain prediction. Meanwhile, the existing of unobserved confounders which affect the input features and labels simultaneously cause spurious correlation and hinder the learning of the invariant relationship contained in the conditional distribution. Interestingly, with a causal view on the data generating process, we find that the input features of one domain are valid instrumental variables for other domains. Inspired by this finding, we propose an instrumental variable-driven DG method (IV-DG) by removing the bias of the unobserved confounders with two-stage learning. In the first stage, it learns the conditional distribution of the input features of one domain given input features of another domain. In the second stage, it estimates the relationship by predicting labels with the learned conditional distribution. Theoretical analyses and simulation experiments show that it accurately captures the invariant relationship. Extensive experiments on real-world datasets demonstrate that IV-DG method yields state-of-the-art results.
Domain generalization (DG) is about learning models that generalize well to new domains that are related to, but different from, the training domain(s). It is a fundamental problem in machine learning and has attracted much attention in recent years. A large number of approaches have been proposed. Different approaches are motivated from different perspectives, making it difficult to gain an overall understanding of the area. In this paper, we propose a causal framework for domain generalization and present an understanding of common DG approaches in the framework. Our work sheds new lights on the following questions: (1) What are the key ideas behind each DG method? (2) Why is it expected to improve generalization to new domains theoretically? (3) How are different DG methods related to each other and what are relative advantages and limitations? By providing a unified perspective on DG, we hope to help researchers better understand the underlying principles and develop more effective approaches for this critical problem in machine learning.
Though Self-supervised learning (SSL) has been widely studied as a promising technique for representation learning, it doesn't generalize well on long-tailed datasets due to the majority classes dominating the feature space. Recent work shows that the long-tailed learning performance could be boosted by sampling extra in-domain (ID) data for self-supervised training, however, large-scale ID data which can rebalance the minority classes are expensive to collect. In this paper, we propose an alternative but easy-to-use and effective solution, Contrastive with Out-of-distribution (OOD) data for Long-Tail learning (COLT), which can effectively exploit OOD data to dynamically re-balance the feature space. We empirically identify the counter-intuitive usefulness of OOD samples in SSL long-tailed learning and principally design a novel SSL method. Concretely, we first localize the `head' and `tail' samples by assigning a tailness score to each OOD sample based on its neighborhoods in the feature space. Then, we propose an online OOD sampling strategy to dynamically re-balance the feature space. Finally, we enforce the model to be capable of distinguishing ID and OOD samples by a distribution-level supervised contrastive loss. Extensive experiments are conducted on various datasets and several state-of-the-art SSL frameworks to verify the effectiveness of the proposed method. The results show that our method significantly improves the performance of SSL on long-tailed datasets by a large margin, and even outperforms previous work which uses external ID data. Our code is available at //github.com/JianhongBai/COLT.
In this paper, we provide a novel framework for the analysis of generalization error of first-order optimization algorithms for statistical learning when the gradient can only be accessed through partial observations given by an oracle. Our analysis relies on the regularity of the gradient w.r.t. the data samples, and allows to derive near matching upper and lower bounds for the generalization error of multiple learning problems, including supervised learning, transfer learning, robust learning, distributed learning and communication efficient learning using gradient quantization. These results hold for smooth and strongly-convex optimization problems, as well as smooth non-convex optimization problems verifying a Polyak-Lojasiewicz assumption. In particular, our upper and lower bounds depend on a novel quantity that extends the notion of conditional standard deviation, and is a measure of the extent to which the gradient can be approximated by having access to the oracle. As a consequence, our analysis provides a precise meaning to the intuition that optimization of the statistical learning objective is as hard as the estimation of its gradient. Finally, we show that, in the case of standard supervised learning, mini-batch gradient descent with increasing batch sizes and a warm start can reach a generalization error that is optimal up to a multiplicative factor, thus motivating the use of this optimization scheme in practical applications.
Deep neural networks (DNNs) may suffer from significantly degenerated performance when the training and test data are of different underlying distributions. Despite the importance of model generalization to out-of-distribution (OOD) data, the accuracy of state-of-the-art (SOTA) models on OOD data can plummet. Recent work has demonstrated that regular or off-manifold adversarial examples, as a special case of data augmentation, can be used to improve OOD generalization. Inspired by this, we theoretically prove that on-manifold adversarial examples can better benefit OOD generalization. Nevertheless, it is nontrivial to generate on-manifold adversarial examples because the real manifold is generally complex. To address this issue, we proposed a novel method of Augmenting data with Adversarial examples via a Wavelet module (AdvWavAug), an on-manifold adversarial data augmentation technique that is simple to implement. In particular, we project a benign image into a wavelet domain. With the assistance of the sparsity characteristic of wavelet transformation, we can modify an image on the estimated data manifold. We conduct adversarial augmentation based on AdvProp training framework. Extensive experiments on different models and different datasets, including ImageNet and its distorted versions, demonstrate that our method can improve model generalization, especially on OOD data. By integrating AdvWavAug into the training process, we have achieved SOTA results on some recent transformer-based models.
Despite the advancement of machine learning techniques in recent years, state-of-the-art systems lack robustness to "real world" events, where the input distributions and tasks encountered by the deployed systems will not be limited to the original training context, and systems will instead need to adapt to novel distributions and tasks while deployed. This critical gap may be addressed through the development of "Lifelong Learning" systems that are capable of 1) Continuous Learning, 2) Transfer and Adaptation, and 3) Scalability. Unfortunately, efforts to improve these capabilities are typically treated as distinct areas of research that are assessed independently, without regard to the impact of each separate capability on other aspects of the system. We instead propose a holistic approach, using a suite of metrics and an evaluation framework to assess Lifelong Learning in a principled way that is agnostic to specific domains or system techniques. Through five case studies, we show that this suite of metrics can inform the development of varied and complex Lifelong Learning systems. We highlight how the proposed suite of metrics quantifies performance trade-offs present during Lifelong Learning system development - both the widely discussed Stability-Plasticity dilemma and the newly proposed relationship between Sample Efficient and Robust Learning. Further, we make recommendations for the formulation and use of metrics to guide the continuing development of Lifelong Learning systems and assess their progress in the future.
Analyzing observational data from multiple sources can be useful for increasing statistical power to detect a treatment effect; however, practical constraints such as privacy considerations may restrict individual-level information sharing across data sets. This paper develops federated methods that only utilize summary-level information from heterogeneous data sets. Our federated methods provide doubly-robust point estimates of treatment effects as well as variance estimates. We derive the asymptotic distributions of our federated estimators, which are shown to be asymptotically equivalent to the corresponding estimators from the combined, individual-level data. We show that to achieve these properties, federated methods should be adjusted based on conditions such as whether models are correctly specified and stable across heterogeneous data sets.
In the domain generalization literature, a common objective is to learn representations independent of the domain after conditioning on the class label. We show that this objective is not sufficient: there exist counter-examples where a model fails to generalize to unseen domains even after satisfying class-conditional domain invariance. We formalize this observation through a structural causal model and show the importance of modeling within-class variations for generalization. Specifically, classes contain objects that characterize specific causal features, and domains can be interpreted as interventions on these objects that change non-causal features. We highlight an alternative condition: inputs across domains should have the same representation if they are derived from the same object. Based on this objective, we propose matching-based algorithms when base objects are observed (e.g., through data augmentation) and approximate the objective when objects are not observed (MatchDG). Our simple matching-based algorithms are competitive to prior work on out-of-domain accuracy for rotated MNIST, Fashion-MNIST, PACS, and Chest-Xray datasets. Our method MatchDG also recovers ground-truth object matches: on MNIST and Fashion-MNIST, top-10 matches from MatchDG have over 50% overlap with ground-truth matches.
Learning disentanglement aims at finding a low dimensional representation which consists of multiple explanatory and generative factors of the observational data. The framework of variational autoencoder (VAE) is commonly used to disentangle independent factors from observations. However, in real scenarios, factors with semantics are not necessarily independent. Instead, there might be an underlying causal structure which renders these factors dependent. We thus propose a new VAE based framework named CausalVAE, which includes a Causal Layer to transform independent exogenous factors into causal endogenous ones that correspond to causally related concepts in data. We further analyze the model identifiabitily, showing that the proposed model learned from observations recovers the true one up to a certain degree. Experiments are conducted on various datasets, including synthetic and real word benchmark CelebA. Results show that the causal representations learned by CausalVAE are semantically interpretable, and their causal relationship as a Directed Acyclic Graph (DAG) is identified with good accuracy. Furthermore, we demonstrate that the proposed CausalVAE model is able to generate counterfactual data through "do-operation" to the causal factors.
This paper focuses on the expected difference in borrower's repayment when there is a change in the lender's credit decisions. Classical estimators overlook the confounding effects and hence the estimation error can be magnificent. As such, we propose another approach to construct the estimators such that the error can be greatly reduced. The proposed estimators are shown to be unbiased, consistent, and robust through a combination of theoretical analysis and numerical testing. Moreover, we compare the power of estimating the causal quantities between the classical estimators and the proposed estimators. The comparison is tested across a wide range of models, including linear regression models, tree-based models, and neural network-based models, under different simulated datasets that exhibit different levels of causality, different degrees of nonlinearity, and different distributional properties. Most importantly, we apply our approaches to a large observational dataset provided by a global technology firm that operates in both the e-commerce and the lending business. We find that the relative reduction of estimation error is strikingly substantial if the causal effects are accounted for correctly.