Bao Duong

Toan Nguyen, Kien Do, Duc Thanh Nguyen et al.

Out-of-distribution (OOD) generalisation aims to build a model that can generalise well on an unseen target domain using knowledge from multiple source domains. To this end, the model should seek the causal dependence between inputs and labels, which may be determined by the semantics of inputs and remain invariant across domains. However, statistical or non-causal methods often cannot capture this dependence and perform poorly due to not considering spurious correlations learnt from model training via unobserved confounders. A well-known existing causal inference method like back-door adjustment cannot be applied to remove spurious correlations as it requires the observation of confounders. In this paper, we propose a novel method that effectively deals with hidden confounders by successfully implementing front-door adjustment (FA). FA requires the choice of a mediator, which we regard as the semantic information of images that helps access the causal mechanism without the need for observing confounders. Further, we propose to estimate the combination of the mediator with other observed images in the front-door formula via style transfer algorithms. Our use of style transfer to estimate FA is novel and sensible for OOD generalisation, which we justify by extensive experimental results on widely used benchmark datasets.

Azhar Mohammed, Dang Nguyen, Bao Duong et al.

Data augmentation is one of the most successful techniques to improve the classification accuracy of machine learning models in computer vision. However, applying data augmentation to tabular data is a challenging problem since it is hard to generate synthetic samples with labels. In this paper, we propose an efficient classifier with a novel data augmentation technique for tabular data. Our method called CCRAL combines causal reasoning to learn counterfactual samples for the original training samples and active learning to select useful counterfactual samples based on a region of uncertainty. By doing this, our method can maximize our model's generalization on the unseen testing data. We validate our method analytically, and compare with the standard baselines. Our experimental results highlight that CCRAL achieves significantly better performance than those of the baselines across several real-world tabular datasets in terms of accuracy and AUC. Data and source code are available at: https://github.com/nphdang/CCRAL.

Toan Nguyen, Kien Do, Bao Duong et al.

We propose a novel approach for domain generalisation (DG) leveraging risk distributions to characterise domains, thereby achieving domain invariance. In our findings, risk distributions effectively highlight differences between training domains and reveal their inherent complexities. In testing, we may observe similar, or potentially intensifying in magnitude, divergences between risk distributions. Hence, we propose a compelling proposition: Minimising the divergences between risk distributions across training domains leads to robust invariance for DG. The key rationale behind this concept is that a model, trained on domain-invariant or stable features, may consistently produce similar risk distributions across various domains. Building upon this idea, we propose Risk Distribution Matching (RDM). Using the maximum mean discrepancy (MMD) distance, RDM aims to minimise the variance of risk distributions across training domains. However, when the number of domains increases, the direct optimisation of variance leads to linear growth in MMD computations, resulting in inefficiency. Instead, we propose an approximation that requires only one MMD computation, by aligning just two distributions: that of the worst-case domain and the aggregated distribution from all domains. Notably, this method empirically outperforms optimising distributional variance while being computationally more efficient. Unlike conventional DG matching algorithms, RDM stands out for its enhanced efficacy by concentrating on scalar risk distributions, sidestepping the pitfalls of high-dimensional challenges seen in feature or gradient matching. Our extensive experiments on standard benchmark datasets demonstrate that RDM shows superior generalisation capability over state-of-the-art DG methods.

Bao Duong, Thin Nguyen

Mutual Information (MI) and Conditional Mutual Information (CMI) are multi-purpose tools from information theory that are able to naturally measure the statistical dependencies between random variables, thus they are usually of central interest in several statistical and machine learning tasks, such as conditional independence testing and representation learning. However, estimating CMI, or even MI, is infamously challenging due the intractable formulation. In this study, we introduce DINE (Diffeomorphic Information Neural Estimator)-a novel approach for estimating CMI of continuous random variables, inspired by the invariance of CMI over diffeomorphic maps. We show that the variables of interest can be replaced with appropriate surrogates that follow simpler distributions, allowing the CMI to be efficiently evaluated via analytical solutions. Additionally, we demonstrate the quality of the proposed estimator in comparison with state-of-the-arts in three important tasks, including estimating MI, CMI, as well as its application in conditional independence testing. The empirical evaluations show that DINE consistently outperforms competitors in all tasks and is able to adapt very well to complex and high-dimensional relationships.

Bao Duong, Thin Nguyen

Detecting conditional independencies plays a key role in several statistical and machine learning tasks, especially in causal discovery algorithms. In this study, we introduce LCIT (Latent representation based Conditional Independence Test)-a novel non-parametric method for conditional independence testing based on representation learning. Our main contribution involves proposing a generative framework in which to test for the independence between X and Y given Z, we first learn to infer the latent representations of target variables X and Y that contain no information about the conditioning variable Z. The latent variables are then investigated for any significant remaining dependencies, which can be performed using the conventional partial correlation test. The empirical evaluations show that LCIT outperforms several state-of-the-art baselines consistently under different evaluation metrics, and is able to adapt really well to both non-linear and high-dimensional settings on a diverse collection of synthetic and real data sets.

Nu Hoang, Bao Duong, Thin Nguyen

Bayesian causal discovery offers the power to quantify epistemic uncertainties among a broad range of structurally diverse causal theories potentially explaining the data, represented in forms of directed acyclic graphs (DAGs). However, existing methods struggle with efficient DAG sampling due to the complex acyclicity constraint. In this study, we propose a scalable Bayesian approach to effectively learn the posterior distribution over causal graphs given observational data thanks to the ability to generate DAGs without explicitly enforcing acyclicity. Specifically, we introduce a novel differentiable DAG sampling method that can generate a valid acyclic causal graph by mapping an unconstrained distribution of implicit topological orders to a distribution over DAGs. Given this efficient DAG sampling scheme, we are able to model the posterior distribution over causal graphs using a simple variational distribution over a continuous domain, which can be learned via the variational inference framework. Extensive empirical experiments on both simulated and real datasets demonstrate the superior performance of the proposed model compared to several state-of-the-art baselines.

Bao Duong, Thin Nguyen

Heretofore, learning the directed acyclic graphs (DAGs) that encode the cause-effect relationships embedded in observational data is a computationally challenging problem. A recent trend of studies has shown that it is possible to recover the DAGs with polynomial time complexity under the equal variances assumption. However, this prohibits the heteroscedasticity of the noise, which allows for more flexible modeling capabilities, but at the same time is substantially more challenging to handle. In this study, we tackle the heteroscedastic causal structure learning problem under Gaussian noises. By exploiting the normality of the causal mechanisms, we can recover a valid causal ordering, which can uniquely identify the causal DAG using a series of conditional independence tests. The result is HOST (Heteroscedastic causal STructure learning), a simple yet effective causal structure learning algorithm that scales polynomially in both sample size and dimensionality. In addition, via extensive empirical evaluations on a wide range of both controlled and real datasets, we show that the proposed HOST method is competitive with state-of-the-art approaches in both the causal order learning and structure learning problems.

Nu Hoang, Bao Duong, Thin Nguyen

Post-nonlinear (PNL) causal models stand out as a versatile and adaptable framework for modeling intricate causal relationships. However, accurately capturing the invertibility constraint required in PNL models remains challenging in existing studies. To address this problem, we introduce CAF-PoNo (Causal discovery via Normalizing Flows for Post-Nonlinear models), harnessing the power of the normalizing flows architecture to enforce the crucial invertibility constraint in PNL models. Through normalizing flows, our method precisely reconstructs the hidden noise, which plays a vital role in cause-effect identification through statistical independence testing. Furthermore, the proposed approach exhibits remarkable extensibility, as it can be seamlessly expanded to facilitate multivariate causal discovery via causal order identification, empowering us to efficiently unravel complex causal relationships. Extensive experimental evaluations on both simulated and real datasets consistently demonstrate that the proposed method outperforms several state-of-the-art approaches in both bivariate and multivariate causal discovery tasks.

Bao Duong, Sunil Gupta, Thin Nguyen

Existing score-based methods for directed acyclic graph (DAG) learning from observational data struggle to recover the causal graph accurately and sample-efficiently. To overcome this, in this study, we propose DrBO (DAG recovery via Bayesian Optimization)-a novel DAG learning framework leveraging Bayesian optimization (BO) to find high-scoring DAGs. We show that, by sophisticatedly choosing the promising DAGs to explore, we can find higher-scoring ones much more efficiently. To address the scalability issues of conventional BO in DAG learning, we replace Gaussian Processes commonly employed in BO with dropout neural networks, trained in a continual manner, which allows for (i) flexibly modeling the DAG scores without overfitting, (ii) incorporation of uncertainty into the estimated scores, and (iii) scaling with the number of evaluations. As a result, DrBO is computationally efficient and can find the accurate DAG in fewer trials and less time than existing state-of-the-art methods. This is demonstrated through an extensive set of empirical evaluations on many challenging settings with both synthetic and real data. Our implementation is available at https://github.com/baosws/DrBO.

Quang-Duy Tran, Bao Duong, Phuoc Nguyen et al.

Distinguishing the cause and effect from bivariate observational data is the foundational problem that finds applications in many scientific disciplines. One solution to this problem is assuming that cause and effect are generated from a structural causal model, enabling identification of the causal direction after estimating the model in each direction. The heteroscedastic noise model is a type of structural causal model where the cause can contribute to both the mean and variance of the noise. Current methods for estimating heteroscedastic noise models choose the Gaussian likelihood as the optimization objective which can be suboptimal and unstable when the data has a non-Gaussian distribution. To address this limitation, we propose a novel approach to estimating this model with Student's $t$-distribution, which is known for its robustness in accounting for sampling variability with smaller sample sizes and extreme values without significantly altering the overall distribution shape. This adaptability is beneficial for capturing the parameters of the noise distribution in heteroscedastic noise models. Our empirical evaluations demonstrate that our estimators are more robust and achieve better overall performance across synthetic and real benchmarks.

Quang-Duy Tran, Phuoc Nguyen, Bao Duong et al.

Score-based approaches in the structure learning task are thriving because of their scalability. Continuous relaxation has been the key reason for this advancement. Despite achieving promising outcomes, most of these methods are still struggling to ensure that the graphs generated from the latent space are acyclic by minimizing a defined score. There has also been another trend of permutation-based approaches, which concern the search for the topological ordering of the variables in the directed acyclic graph in order to limit the search space of the graph. In this study, we propose an alternative approach for strictly constraining the acyclicty of the graphs with an integration of the knowledge from the topological orderings. Our approach can reduce inference complexity while ensuring the structures of the generated graphs to be acyclic. Our empirical experiments with simulated and real-world data show that our approach can outperform related Bayesian score-based approaches.