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Causal discovery witnessed significant progress over the past decades. In particular,many recent causal discovery methods make use of independent, non-Gaussian noise to achieve identifiability of the causal models. Existence of hidden direct common causes, or confounders, generally makes causal discovery more difficult;whenever they are present, the corresponding causal discovery algorithms canbe seen as extensions of overcomplete independent component analysis (OICA). However, existing OICA algorithms usually make strong parametric assumptions on the distribution of independent components, which may be violated on real data, leading to sub-optimal or even wrong solutions. In addition, existing OICA algorithms rely on the Expectation Maximization (EM) procedure that requires computationally expensive inference of the posterior distribution of independent components. To tackle these problems, we present a Likelihood-Free Overcomplete ICA algorithm (LFOICA1) that estimates the mixing matrix directly byback-propagation without any explicit assumptions on the density function of independent components. Thanks to its computational efficiency, the proposed method makes a number of causal discovery procedures much more practically feasible.For illustrative purposes, we demonstrate the computational efficiency and efficacy of our method in two causal discovery tasks on both synthetic and real data. 

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. 

Learning causal structure from observational data has attracted much attention,and it is notoriously challenging to find the underlying structure in the presenceof confounders (hidden direct common causes of two variables). In this paper,by properly leveraging the non-Gaussianity of the data, we propose to estimatethe structure over latent variables with the so-called Triad constraints: we design a form of "pseudo-residual" from three variables, and show that when causal relations are linear and noise terms are non-Gaussian, the causal direction between the latent variables for the three observed variables is identifiable by checking a certain kind of independence relationship. In other words, the Triad constraints help us to locate latent confounders and determine the causal direction between them. This goes far beyond the Tetrad constraints and reveals more information about the underlying structure from non-Gaussian data. Finally, based on the Triad constraints, we develop a two-step algorithm to learn the causal structure corresponding to measurement models. Experimental results on both synthetic and real data demonstrate the effectiveness and reliability of our method. 

Identification of causal direction between a causal-effect pair from observed data has recently attracted much attention. Various methods based on functional causal models have been proposed to solve this problem, by assuming the causal process satisfies some (structural) constraints and showing that the reverse direction violates such constraints. The nonlinear additive noise model has been demonstrated to be effective for this purpose, but the model class is not transitive--even if each direct causal relation follows this model, indirect causal influences, which result from omitted intermediate causal variables and are frequently encountered in practice, do not necessarily follow the model constraints; as a consequence, the nonlinear additive noise model may fail to correctly discover causal direction. In this work, we propose a cascade nonlinear additive noise model to represent such causal influences--each direct causal relation follows the nonlinear additive noise model but we observe only the initial cause and final effect. We further propose a method to estimate the model, including the unmeasured intermediate variables, from data, under the variational auto-encoder framework. Our theoretical results show that with our model, causal direction is identifiable under suitable technical conditions on the data generation process. Simulation results illustrate the power of the proposed method in identifying indirect causal relations across various settings, and experimental results on real data suggest that the proposed model and method greatly extend the applicability of causal discovery based on functional causal models in nonlinear cases.

 

Domain adaptation is an important but challenging task. Most of the existing domain adaptation methods struggle to extract the domain-invariant representation on the feature space with entangling domain information and semantic information. Different from previous efforts on the entangled feature space, we aim to extract the domain invariant semantic information in the latent disentangled semantic representation (DSR) of the data. In DSR, we assume the data generation process is controlled by two independent sets of variables, i.e., the semantic latent variables and the domain latent variables. Under the above assumption, we employ a variational auto-encoder to reconstruct the semantic latent variables and domain latent variables behind the data. We further devise a dual adversarial network to disentangle these two sets of reconstructed latent variables. The disentangled semantic latent variables are finally adapted across the domains. Experimental studies testify that our model yields state-of-the-art performance on several domain adaptation benchmark datasets.

 

Missing data are ubiquitous in many domain such as healthcare. When these data entries are not missing completely at random, the (conditional) independence relations in the observed data may be different from those in the complete data generated by the underlying causal process.Consequently, simply applying existing causal discovery methods to the observed data may lead to wrong conclusions. In this paper, we aim at developing a causal discovery method to recover the underlying causal structure from observed data that are missing under different mechanisms, including missing completely at random (MCAR),missing at random (MAR), and missing not at random (MNAR). With missingness mechanisms represented by missingness graphs (m-graphs),we analyze conditions under which additional correction is needed to derive conditional independence/dependence relations in the complete data. Based on our analysis, we propose Miss-ing Value PC (MVPC), which extends the PC algorithm to incorporate additional corrections.Our proposed MVPC is shown in theory to give asymptotically correct results even on data that are MAR or MNAR. Experimental results on both synthetic data and real healthcare applications illustrate that the proposed algorithm is able to find correct causal relations even in the general case of MNAR. 

A key problem in domain adaptation is determining what to transfer across different domains. We propose a data-driven method to represent these changes across multiple source domains and perform unsupervised domain adaptation. We assume that the joint distributions follow a specific generating process and have a small number of identifiable changing parameters, and develop a data-driven method to identify the changing parameters by learning low-dimensional representations of the changing class-conditional distributions across multiple source domains. The learned low-dimensional representations enable us to reconstruct the target-domain joint distribution from unlabeled target-domain data, and further enable predicting the labels in the target domain. We demonstrate the efficacy of this method by conducting experiments on synthetic and real datasets.