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In many prediction problems, spurious correlations are induced by a changing relationship between the label and a nuisance variable that is also correlated with the covariates. For example, in classifying animals in natural images, the background, which is a nuisance, can predict the type of animal. This nuisance-label relationship does not always hold, and the performance of a model trained under one such relationship may be poor on data with a different nuisance-label relationship. To build predictive models that perform well regardless of the nuisance-label relationship, we develop Nuisance-Randomized Distillation (NURD). We introduce the nuisance-randomized distribution, a distribution where the nuisance and the label are independent. Under this distribution, we define the set of representations such that conditioning on any member, the nuisance and the label remain independent. We prove that the representations in this set always perform better than chance, while representations outside of this set may not. NURD finds a representation from this set that is most informative of the label under the nuisance-randomized distribution, and we prove that this representation achieves the highest performance regardless of the nuisance-label relationship. We evaluate NURD on several tasks including chest X-ray classification where, using non-lung patches as the nuisance, NURD produces models that predict pneumonia under strong spurious correlations. 

Comparing the inferences of diverse candidate models is an essential part of model checking and escaping local optima. To enable efficient comparison, we introduce an amortized variational inference framework that can perform fast and reliable posterior estimation across models of the same architecture. Our Any Parameter Encoder (APE) extends the encoder neural network common in amortized inference to take both a data feature vector and a model parameter vector as input. APE thus reduces posterior inference across unseen data and models to a single forward pass. In experiments comparing candidate topic models for synthetic data and product reviews, our Any Parameter Encoder yields comparable posteriors to more expensive methods in far less time, especially when the encoder architecture is designed in model-aware fashion. 

Comparing the inferences of diverse candidate models is an essential part of model checking and escaping local optima. To enable efficient comparison, we introduce an amortized variational inference framework that can perform fast and reliable posterior estimation across models of the same architecture. Our Any Parameter Encoder (APE) extends the encoder neural network common in amortized inference to take both a data feature vector and a model parameter vector as input. APE thus reduces posterior inference across unseen data and models to a single forward pass. In experiments comparing candidate topic models for synthetic data and product reviews, our Any Parameter Encoder yields comparable posteriors to more expensive methods in far less time, especially when the encoder architecture is designed in model-aware fashion.