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Unpaired image-to-image translation (I2I) is an ill-posed problem, as an infinite number of translation functions can map the source domain distribution to the target distribution. Therefore, much effort has been put into designing suitable constraints, e.g., cycle consistency (CycleGAN), geometry consistency (GCGAN), and contrastive learning-based constraints (CUTGAN), that help better pose the problem. However, these well-known constraints have limitations: (1) they are either too restrictive or too weak for specific I2I tasks; (2) these methods result in content distortion when there is a significant spatial variation between the source and target domains. This paper proposes a universal regularization technique called maximum spatial perturbation consistency (MSPC), which enforces a spatial perturbation function (T) and the translation operator (G) to be commutative (i.e., T \circ G = G \circ T ). In addition, we introduce two adversarial training components for learning the spatial perturbation function. The first one lets T compete with G to achieve maximum perturbation. The second one lets G and T compete with discriminators to align the spatial variations caused by the change of object size, object distortion, background interruptions, etc. Our method outperforms the state-of-the-art methods on most I2I benchmarks. We also introduce a new benchmark, namely the front face to profile face dataset, to emphasize the underlying challenges of I2I for real-world applications. We finally perform ablation experiments to study the sensitivity of our method to the severity of spatial perturbation and its effectiveness for distribution alignment. 

Discovery of causal relations from observational data is essential for many disciplines of science and real-world applications. However, unlike other machine learning algorithms, whose development has been greatly fostered by a large amount of available benchmark datasets, causal discovery algorithms are notoriously difficult to be systematically evaluated because few datasets with known ground-truth causal relations are available. In this work, we handle the problem of evaluating causal discovery algorithms by building a flexible simulator in the medical setting. We develop a neuropathic pain diagnosis simulator, inspired by the fact that the biological processes of neuropathic pathophysiology are well studied with well-understood causal influences. Our simulator exploits the causal graph of theneuropathic pain pathology and its parameters in the generator are estimated from real-life patient cases. We show that the data generated from our simulator have similar statistics as real-world data. As a clear advantage, the simulator can produce infinite samples without jeopardizing the privacy of real-world patients. Our simulator provides a natural tool for evaluating various types of causal discovery algorithms, including those to deal with practical issues in causal discovery, such as unknown confounders, selection bias, and missing data. Using our simulator,we have evaluated extensively causal discovery algorithms under various settings. 

State-of-the-art approaches to causal discovery usually assume a fixed underlying causal model. However, it is often the case that causal models vary across domains or subjects, due to possibly omitted factors that affect the quantitative causal effects. As a typical example, causal connectivity in the brain network has been reported to vary across individuals, with significant differences across groups of people, such as autistics and typical controls. In this paper, we develop a unified framework for causal discovery and mechanism-based group identification. In particular, we propose a specific and shared causal model (SSCM), which takes into account the variabilities of causal relations across individuals/groups and leverages their commonalities to achieve statistically reliable estimation. The learned SSCM gives the specific causal knowledge for each individual as well as the general trend over the population. In addition, the estimated model directly provides the group information of each individual. Experimental results on synthetic and real-world data demonstrate the efficacy of the proposed method. 

Domain generalization (DG) aims to incorporate knowledge from multiple source domains into a single model that could generalize well on unseen target domains. This problem is ubiquitous in practice since the distributions of the target data may rarely be identical to those of the source data. In this paper, we propose Multidomain Discriminant Analysis (MDA) to address DG of classification tasks in general situations. MDA learns a domain-invariant feature transformation that aims to achieve appealing properties, including a minimal divergence among domains within each class, a maximal separability among classes, and overall maximal compactness of all classes. Furthermore, we provide the bounds on excess risk and generalization error by learning theory analysis. Comprehensive experiments on synthetic and real benchmark datasets demonstrate the effectiveness of MDA. 

In many scientific fields, such as economics and neuroscience, we are often faced with nonstationary time series, and concerned with both finding causal relations and forecasting the values of variables of interest, both of which are particularly challenging in such nonstationary environments. In this paper, we study causal discovery and forecasting for nonstationary time series. By exploiting a particular type of state-space model to represent the processes, we show that nonstationarity helps to identify the causal structure, and that forecasting naturally benefits from learned causal knowledge. Specifically, we allow changes in both causal strengths and noise variances in the nonlinear state-space models, which, interestingly, renders both the causal structure and model parameters identifiable. Given the causal model, we treat forecasting as a problem in Bayesian inference in the causal model, which exploits the time-varying property of the data and adapts to new observations in a principled manner. Experimental results on synthetic and real-world data sets demonstrate the efficacy of the proposed methods. 

We consider the problem of inferring causal relationships between two or more passively ob-served variables. While the problem of such causal discovery has been extensively studied,especially in the bivariate setting, the majority of current methods assume a linear causal relationship, and the few methods which consider non-linear relations usually make the assumption of additive noise. Here, we propose a framework through which we can perform causal discovery in the presence of general nonlinear relationships. The proposed method is based on recent progress in non-linear in-dependent component analysis (ICA) and exploits the nonstationarity of observations in order to recover the underlying sources. We show rigorously that in the case of bivariate causal discovery, such non-linear ICA can be used to infer causal direction via a series of in-dependence tests. We further propose an alternative measure for inferring causal direction based on asymptotic approximations to the likelihood ratio, as well as an extension to multivariate causal discovery. We demonstrate the capabilities of the proposed method via a series of simulation studies and conclude with an application to neuroimaging data.