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We introduce Invariant Risk Minimization (IRM), a learning paradigm to estimate invariant correlations across multiple training distributions. To achieve this goal, IRM learns a data representation such that the optimal classifier, on top of that data representation, matches for all training distributions. Through theory and experiments, we show how the invariances learned by IRM relate to the causal structures governing the data and enable out-of-distribution generalization.
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We show that the Invariant Risk Minimization (IRM) formulation of Arjovsky et al. (2019) can fail to capture natural invariances, at least when used in its practical linear form, and even on very simple problems which directly follow the motivating examples for IRM. This can lead to worse generalization on new environments, even when compared to unconstrained ERM. The issue stems from a significant gap between the linear variant (as in their concrete method IRMv1) and the full non-linear IRM formulation. Additionally, even when capturing the right invariances, we show that it is possible for IRM to learn a sub-optimal predictor, due to the loss function not being invariant across environments. The issues arise even when measuring invariance on the population distributions, but are exacerbated by the fact that IRM is extremely fragile to sampling.
Empirical Risk Minimization (ERM) based machine learning algorithms have suffered from weak generalization performance on data obtained from out-of-distribution (OOD). To address this problem, Invariant Risk Minimization (IRM) objective was suggested to find invariant optimal predictor which is less affected by the changes in data distribution. However, even with such progress, IRMv1, the practical formulation of IRM, still shows performance degradation when there are not enough training data, and even fails to generalize to OOD, if the number of spurious correlations is larger than the number of environments. In this paper, to address such problems, we propose a novel meta-learning based approach for IRM. In this method, we do not assume the linearity of classifier for the ease of optimization, and solve ideal bi-level IRM objective with Model-Agnostic Meta-Learning (MAML) framework. Our method is more robust to the data with spurious correlations and can provide an invariant optimal classifier even when data from each distribution are scarce. In experiments, we demonstrate that our algorithm not only has better OOD generalization performance than IRMv1 and all IRM variants, but also addresses the weakness of IRMv1 with improved stability.
The standard risk minimization paradigm of machine learning is brittle when operating in environments whose test distributions are different from the training distribution due to spurious correlations. Training on data from many environments and finding invariant predictors reduces the effect of spurious features by concentrating models on features that have a causal relationship with the outcome. In this work, we pose such invariant risk minimization as finding the Nash equilibrium of an ensemble game among several environments. By doing so, we develop a simple training algorithm that uses best response dynamics and, in our experiments, yields similar or better empirical accuracy with much lower variance than the challenging bi-level optimization problem of Arjovsky et al. (2019). One key theoretical contribution is showing that the set of Nash equilibria for the proposed game are equivalent to the set of invariant predictors for any finite number of environments, even with nonlinear classifiers and transformations. As a result, our method also retains the generalization guarantees to a large set of environments shown in Arjovsky et al. (2019). The proposed algorithm adds to the collection of successful game-theoretic machine learning algorithms such as generative adversarial networks.
Privacy concern has been increasingly important in many machine learning (ML) problems. We study empirical risk minimization (ERM) problems under secure multi-party computation (MPC) frameworks. Main technical tools for MPC have been developed based on cryptography. One of limitations in current cryptographically private ML is that it is computationally intractable to evaluate non-linear functions such as logarithmic functions or exponential functions. Therefore, for a class of ERM problems such as logistic regression in which non-linear function evaluations are required, one can only obtain approximate solutions. In this paper, we introduce a novel cryptographically private tool called secure approximation guarantee (SAG) method. The key property of SAG method is that, given an arbitrary approximate solution, it can provide a non-probabilistic assumption-free bound on the approximation quality under cryptographically secure computation framework. We demonstrate the benefit of the SAG method by applying it to several problems including a practical privacy-preserving data analysis task on genomic and clinical information.
Inferring causal individual treatment effect (ITE) from observational data is a challenging problem whose difficulty is exacerbated by the presence of treatment assignment bias. In this work, we propose a new way to estimate the ITE using the domain generalization framework of invariant risk minimization (IRM). IRM uses data from multiple domains, learns predictors that do not exploit spurious domain-dependent factors, and generalizes better to unseen domains. We propose an IRM-based ITE estimator aimed at tackling treatment assignment bias when there is little support overlap between the control group and the treatment group. We accomplish this by creating diversity: given a single dataset, we split the data into multiple domains artificially. These diverse domains are then exploited by IRM to more effectively generalize regression-based models to data regions that lack support overlap. We show gains over classical regression approaches to ITE estimation in settings when support mismatch is more pronounced.
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