Conventional supervised learning methods, especially deep ones, are found to be sensitive to out-of-distribution (OOD) examples, largely because the learned representation mixes the semantic factor with the variation factor due to their domain-specific correlation, while only the semantic factor causes the output. To address the problem, we propose a Causal Semantic Generative model (CSG) based on a causal reasoning so that the two factors are modeled separately, and develop methods for OOD prediction from a single training domain, which is common and challenging. The methods are based on the causal invariance principle, with a novel design for both efficient learning and easy prediction. Theoretically, we prove that under certain conditions, CSG can identify the semantic factor by fitting training data, and this semantic-identification guarantees the boundedness of OOD generalization error and the success of adaptation. Empirical study shows improved OOD performance over prevailing baselines.

Learning Causal Semantic Representation for Out-of-Distribution Prediction

Learning under multi-environments often requires the ability of out-of-distribution generalization for the worst-environment performance guarantee. Some novel algorithms, e.g. Invariant Risk Minimization and Risk Extrapolation, build stable models by extracting invariant (causal) feature. However, it remains unclear how these methods learn to remove the environmental features. In this paper, we focus on the Risk Extrapolation (REx) and make attempts to fill this gap. We first propose a framework, Quasi-Distributional Robustness, to unify the Empirical Risk Minimization (ERM), the Robust Optimization (RO) and the Risk Extrapolation. Then, under this framework, we show that, comparing to ERM and RO, REx has a much larger robust region. Furthermore, based on our analysis, we propose a novel regularization method, Risk Variance Penalization (RVP), which is derived from REx. The proposed method is easy to implement, and has proper degree of penalization, and enjoys an interpretable tuning parameter. Finally, our experiments show that under certain conditions, the regularization strategy that encourages the equality of training risks has ability to discover relationships which do not exist in the training data. This provides important evidence to support that RVP is useful to discover causal models.

Risk Variance Penalization: From Distributional Robustness to Causality.

This work considers the out-of-distribution (OOD) prediction problem where (1)~the training data are from multiple domains and (2)~the test domain is unseen in the training. DNNs fail in OOD prediction because they are prone to pick up spurious correlations. Recently, Invariant Risk Minimization (IRM) is proposed to address this issue. Its effectiveness has been demonstrated in the colored MNIST experiment. Nevertheless, we find that the performance of IRM can be dramatically degraded under \emph{strong Λ spuriousness} -- when the spurious correlation between the spurious features and the class label is strong due to the strong causal influence of their common cause, the domain label, on both of them (see Fig. 1). In this work, we try to answer the questions: why does IRM fail in the aforementioned setting? Why does IRM work for the original colored MNIST dataset? Then, we propose a simple and effective approach to fix the problem of IRM. We combine IRM with conditional distribution matching to avoid a specific type of spurious correlation under strong Λ spuriousness. Empirically, we design a series of semi synthetic datasets -- the colored MNIST plus, which exposes the problems of IRM and demonstrates the efficacy of the proposed method.

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Out-of-distribution Prediction with Invariant Risk Minimization: The Limitation and An Effective Fix

Classic machine learning methods are built on the $i.i.d.$ assumption that
training and testing data are independent and identically distributed. However,
in real scenarios, the $i.i.d.$ assumption can hardly be satisfied, rendering
the sharp drop of classic machine learning algorithms' performances under
distributional shifts, which indicates the significance of investigating the
Out-of-Distribution generalization problem. Out-of-Distribution (OOD)
generalization problem addresses the challenging setting where the testing
distribution is unknown and different from the training. This paper serves as
the first effort to systematically and comprehensively discuss the OOD
generalization problem, from the definition, methodology, evaluation to the
implications and future directions. Firstly, we provide the formal definition
of the OOD generalization problem. Secondly, existing methods are categorized
into three parts based on their positions in the whole learning pipeline,
namely unsupervised representation learning, supervised model learning and
optimization, and typical methods for each category are discussed in detail. We
then demonstrate the theoretical connections of different categories, and
introduce the commonly used datasets and evaluation metrics. Finally, we
summarize the whole literature and raise some future directions for OOD
generalization problem. The summary of OOD generalization methods reviewed in
this survey can be found at http://out-of-distribution-generalization.com.

Towards Out-Of-Distribution Generalization: A Survey

Generalization to out-of-distribution (OOD) data, or domain generalization, is one of the central problems in modern machine learning. Recently, there is a surge of attempts to propose algorithms for OOD that mainly build upon the idea of extracting invariant features. Although intuitively reasonable, theoretical understanding of what kind of invariance can guarantee OOD generalization is still limited, and generalization to arbitrary out-of-distribution is clearly impossible. In this work, we take the first step towards rigorous and quantitative definitions of 1) what is OOD; and 2) what does it mean by saying an OOD problem is learnable. We also introduce a new concept of expansion function, which characterizes to what extent the variance is amplified in the test domains over the training domains, and therefore give a quantitative meaning of invariant features. Based on these, we prove OOD generalization error bounds. It turns out that OOD generalization largely depends on the expansion function. As recently pointed out by Gulrajani and Lopez-Paz (2020), any OOD learning algorithm without a model selection module is incomplete. Our theory naturally induces a model selection criterion. Extensive experiments on benchmark OOD datasets demonstrate that our model selection criterion has a significant advantage over baselines.

Towards a Theoretical Framework of Out-of-Distribution Generalization

The mismatch between training dataset and target environment is one major challenge for current machine learning systems When training data is collected from multiple environments and the the evaluation is on any new environment, we are facing an Out-of-Distribution (OOD) generalization problem that aims to find a model with the best OOD accuracy, ie the best worst-environment accuracy However, with limited access to environments, the worst environment may be unseen, and test accuracy is a biased estimate of OOD accuracy In this paper, we show that test accuracy may dramatically fail to identify OOD accuracy and mislead the tuning procedure To this end, we introduce Influence Function, a classical tool from robust statistics, into the OOD generalization problem and suggest the variance of influence function to measure the stability of a model on training environments We show that the proposed index and test accuracy together can help us discern whether OOD algorithms are needed and whether a model achieves good OOD generalization

/pdf/out-of-distribution-generalization-analysis-via-influence-55kfwmhutd.pdf

Out-of-Distribution Generalization Analysis via Influence Function

The key of the out-of-distribution (OOD) generalization is to generalize invariance from training domains to target domains. The variance risk extrapolation (V-REx) is a practical OOD method, which depends on a domain-level regularization but lacks theoretical verifications about its motivation and utility. This article provides theoretical insights into V-REx by studying a variance-based regularizer. We propose Risk Variance Penalization (RVP), which slightly changes the regularization of V-REx but addresses the theory concerns about V-REx. We provide theoretical explanations and a theory-inspired tuning scheme for the regularization parameter of RVP. Our results point out that RVP discovers a robust predictor. Finally, we experimentally show that the proposed regularizer can find an invariant predictor under certain conditions.

Haotian Ye

Papers

Out-of-Distribution Generalization Analysis via Influence Function

Towards a Theoretical Framework of Out-of-Distribution Generalization

Risk Variance Penalization