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.
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In recent years, powered by the learned discriminative representation via graph neural network (GNN) models, deep graph matching methods have made great progresses in the task of matching semantic features. However, these methods usually rely on heuristically generated graph patterns, which may introduce unreliable relationships to hurt the matching performance. In this paper, we propose a joint \emph{graph learning and matching} network, named GLAM, to explore reliable graph structures for boosting graph matching. GLAM adopts a pure attention-based framework for both graph learning and graph matching. Specifically, it employs two types of attention mechanisms, self-attention and cross-attention for the task. The self-attention discovers the relationships between features and to further update feature representations over the learnt structures; and the cross-attention computes cross-graph correlations between the two feature sets to be matched for feature reconstruction. Moreover, the final matching solution is directly derived from the output of the cross-attention layer, without employing a specific matching decision module. The proposed method is evaluated on three popular visual matching benchmarks (Pascal VOC, Willow Object and SPair-71k), and it outperforms previous state-of-the-art graph matching methods by significant margins on all benchmarks. Furthermore, the graph patterns learnt by our model are validated to be able to remarkably enhance previous deep graph matching methods by replacing their handcrafted graph structures with the learnt ones.
Domain generalization aims to learn a prediction model on multi-domain source data such that the model can generalize to a target domain with unknown statistics. Most existing approaches have been developed under the assumption that the source data is well-balanced in terms of both domain and class. However, real-world training data collected with different composition biases often exhibits severe distribution gaps for domain and class, leading to substantial performance degradation. In this paper, we propose a self-balanced domain generalization framework that adaptively learns the weights of losses to alleviate the bias caused by different distributions of the multi-domain source data. The self-balanced scheme is based on an auxiliary reweighting network that iteratively updates the weight of loss conditioned on the domain and class information by leveraging balanced meta data. Experimental results demonstrate the effectiveness of our method overwhelming state-of-the-art works for domain generalization.
We present a Bayesian inference approach to estimating the cumulative mass profile and mean squared velocity profile of a globular cluster given the spatial and kinematic information of its stars. Mock globular clusters with a range of sizes and concentrations are generated from lowered isothermal dynamical models, from which we test the reliability of the Bayesian method to estimate model parameters through repeated statistical simulation. We find that given unbiased star samples, we are able to reconstruct the cluster parameters used to generate the mock cluster and the cluster's cumulative mass and mean velocity squared profiles with good accuracy. We further explore how strongly biased sampling, which could be the result of observing constraints, may affect this approach. Our tests indicate that if we instead have biased samples, then our estimates can be off in certain ways that are dependent on cluster morphology. Overall, our findings motivate obtaining samples of stars that are as unbiased as possible. This may be achieved by combining information from multiple telescopes (e.g., Hubble and Gaia), but will require careful modeling of the measurement uncertainties through a hierarchical model, which we plan to pursue in future work.
Haskell is a popular choice for hosting deeply embedded languages. A recurring challenge for these embeddings is how to seamlessly integrate user defined algebraic data types. In particular, one important, convenient, and expressive feature for creating and inspecting data -- pattern matching -- is not directly available on embedded terms. In this paper, we present a novel technique, embedded pattern matching, which enables a natural and user friendly embedding of user defined algebraic data types into the embedded language. Our technique enables users to pattern match on terms in the embedded language in much the same way they would in the host language.
Existing Unsupervised Domain Adaptation (UDA) literature adopts the covariate shift and conditional shift assumptions, which essentially encourage models to learn common features across domains. However, due to the lack of supervision in the target domain, they suffer from the semantic loss: the feature will inevitably lose non-discriminative semantics in source domain, which is however discriminative in target domain. We use a causal view -- transportability theory -- to identify that such loss is in fact a confounding effect, which can only be removed by causal intervention. However, the theoretical solution provided by transportability is far from practical for UDA, because it requires the stratification and representation of the unobserved confounder that is the cause of the domain gap. To this end, we propose a practical solution: Transporting Causal Mechanisms (TCM), to identify the confounder stratum and representations by using the domain-invariant disentangled causal mechanisms, which are discovered in an unsupervised fashion. Our TCM is both theoretically and empirically grounded. Extensive experiments show that TCM achieves state-of-the-art performance on three challenging UDA benchmarks: ImageCLEF-DA, Office-Home, and VisDA-2017. Codes are available in Appendix.
Approaches based on deep neural networks have achieved striking performance when testing data and training data share similar distribution, but can significantly fail otherwise. Therefore, eliminating the impact of distribution shifts between training and testing data is crucial for building performance-promising deep models. Conventional methods assume either the known heterogeneity of training data (e.g. domain labels) or the approximately equal capacities of different domains. In this paper, we consider a more challenging case where neither of the above assumptions holds. We propose to address this problem by removing the dependencies between features via learning weights for training samples, which helps deep models get rid of spurious correlations and, in turn, concentrate more on the true connection between discriminative features and labels. Extensive experiments clearly demonstrate the effectiveness of our method on multiple distribution generalization benchmarks compared with state-of-the-art counterparts. Through extensive experiments on distribution generalization benchmarks including PACS, VLCS, MNIST-M, and NICO, we show the effectiveness of our method compared with state-of-the-art counterparts.
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.
We investigate the problem of automatically determining what type of shoe left an impression found at a crime scene. This recognition problem is made difficult by the variability in types of crime scene evidence (ranging from traces of dust or oil on hard surfaces to impressions made in soil) and the lack of comprehensive databases of shoe outsole tread patterns. We find that mid-level features extracted by pre-trained convolutional neural nets are surprisingly effective descriptors for this specialized domains. However, the choice of similarity measure for matching exemplars to a query image is essential to good performance. For matching multi-channel deep features, we propose the use of multi-channel normalized cross-correlation and analyze its effectiveness. Our proposed metric significantly improves performance in matching crime scene shoeprints to laboratory test impressions. We also show its effectiveness in other cross-domain image retrieval problems: matching facade images to segmentation labels and aerial photos to map images. Finally, we introduce a discriminatively trained variant and fine-tune our system through our proposed metric, obtaining state-of-the-art performance.
Methods that align distributions by minimizing an adversarial distance between them have recently achieved impressive results. However, these approaches are difficult to optimize with gradient descent and they often do not converge well without careful hyperparameter tuning and proper initialization. We investigate whether turning the adversarial min-max problem into an optimization problem by replacing the maximization part with its dual improves the quality of the resulting alignment and explore its connections to Maximum Mean Discrepancy. Our empirical results suggest that using the dual formulation for the restricted family of linear discriminators results in a more stable convergence to a desirable solution when compared with the performance of a primal min-max GAN-like objective and an MMD objective under the same restrictions. We test our hypothesis on the problem of aligning two synthetic point clouds on a plane and on a real-image domain adaptation problem on digits. In both cases, the dual formulation yields an iterative procedure that gives more stable and monotonic improvement over time.
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