arXiv subjects

Bao Duong

Publications and source records attributed to Bao Duong.

17 recordsLinked to original sources

arXiv2026

Geometry-Aware Bayesian Parameter-Efficient Fine-Tuning on the Stiefel Manifold via Stein Variational Gradient Descent

Several geometry-aware approaches to low-rank adaptation have emerged for parameter-efficient fine-tuning of large pre-trained models. These methods aim to take full advantage of the geometric structure of low-rank manifolds for improving the efficiency in subspace utilization and reducing redundancy by enforcing orthogonality constraints during optimization. The strong empirical results of these techniques have motivated further study into whether predictions from such geometry-based adaptation methods could be overconfident. In this paper, we build on the singular value decomposition factorization of adapters to develop a framework based on Stein variational gradient descent (SVGD). In this formulation, the low-rank matrices are transported along the Stiefel manifold to match the targeted distributions while retaining their crucial geometric structure. Since this geometry-aware SVGD approach provides multiple solutions during inference, it supports uncertainty quantification and produces better-calibrated adapters on the Stiefel manifold. Extensive experiments show that our method delivers strong model calibration and attains higher prediction accuracy than SVGD and related uncertainty estimation methods that are formulated in Euclidean space.

cs.LG↗

arXiv2026

Similarity-Aware Personalized Federated Learning in Heterogeneous Environments

Federated Learning (FL) allows decentralized clients to train models collaboratively while preserving data privacy. However, distribution mismatch across clients often leads to poor global generalization and degraded local client-level performance. In such scenarios, some of the clients with their local models trained solely on local data may perform better than the globally learnt model, thus nullifying the benefits of collaborative federated learning. To address this, we propose SAPE-FL (Similarity-Aware Personalized Federated Learning), a novel personalization framework that anchors each client's model to both the global model and a similarity-weighted peer averaged model. By incorporating dynamic, client-specific regularization based on both model similarity and output similarity, SAPE-FL adaptively balances global knowledge transfer and peer collaboration while filtering out dissimilar clients. This dual anchoring mitigates negative transfer and enhances robustness in heterogeneous settings. We theoretically analyze our algorithm establishing its convergence guarantees and empirically show that SAPE-FL outperforms state-of-the-art methods under high statistical heterogeneity and low client data regimes.

cs.LG↗

arXiv2026

Neural Autoregressive Flows for Markov Boundary Learning

Recovering Markov boundary -- the minimal set of variables that maximizes predictive performance for a response variable -- is crucial in many applications. While recent advances improve upon traditional constraint-based techniques by scoring local causal structures, they still rely on nonparametric estimators and heuristic searches, lacking theoretical guarantees for reliability. This paper investigates a framework for efficient Markov boundary discovery by integrating conditional entropy from information theory as a scoring criterion. We design a novel masked autoregressive network to capture complex dependencies. A parallelizable greedy search strategy in polynomial time is proposed, supported by analytical evidence. We also discuss how initializing a graph with learned Markov boundaries accelerates the convergence of causal discovery. Comprehensive evaluations on real-world and synthetic datasets demonstrate the scalability and superior performance of our method in both Markov boundary discovery and causal discovery tasks.

cs.LG↗

arXiv2025

Identifying Causal Direction via Variational Bayesian Compression

Telling apart the cause and effect between two random variables with purely observational data is a challenging problem that finds applications in various scientific disciplines. A key principle utilized in this task is the algorithmic Markov condition, which postulates that the joint distribution, when factorized according to the causal direction, yields a more succinct codelength compared to the anti-causal direction. Previous approaches approximate these codelengths by relying on simple functions or Gaussian processes (GPs) with easily evaluable complexity, compromising between model fitness and computational complexity. To address these limitations, we propose leveraging the variational Bayesian learning of neural networks as an interpretation of the codelengths. This allows the improvement of model fitness, while maintaining the succinctness of the codelengths, and the avoidance of the significant computational complexity of the GP-based approaches. Extensive experiments on both synthetic and real-world benchmarks in cause-effect identification demonstrate the effectiveness of our proposed method, showing promising performance enhancements on several datasets in comparison to most related methods.

cs.LG↗

arXiv2025

Amortized Conditional Independence Testing

Testing for the conditional independence structure in data is a fundamental and critical task in statistics and machine learning, which finds natural applications in causal discovery - a highly relevant problem to many scientific disciplines. Existing methods seek to design explicit test statistics that quantify the degree of conditional dependence, which is highly challenging yet cannot capture nor utilize prior knowledge in a data-driven manner. In this study, an entirely new approach is introduced, where we instead propose to amortize conditional independence testing and devise ACID - a novel transformer-based neural network architecture that learns to test for conditional independence. ACID can be trained on synthetic data in a supervised learning fashion, and the learned model can then be applied to any dataset of similar natures or adapted to new domains by fine-tuning with a negligible computational cost. Our extensive empirical evaluations on both synthetic and real data reveal that ACID consistently achieves state-of-the-art performance against existing baselines under multiple metrics, and is able to generalize robustly to unseen sample sizes, dimensionalities, as well as non-linearities with a remarkably low inference time.

stat.ML↗

arXiv2025

Causal Discovery via Bayesian Optimization

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.

cs.LG↗

arXiv2024

Reinforcement Learning for Causal Discovery without Acyclicity Constraints

Recently, reinforcement learning (RL) has proved a promising alternative for conventional local heuristics in score-based approaches to learning directed acyclic causal graphs (DAGs) from observational data. However, the intricate acyclicity constraint still challenges the efficient exploration of the vast space of DAGs in existing methods. In this study, we introduce ALIAS (reinforced dAg Learning wIthout Acyclicity conStraints), a novel approach to causal discovery powered by the RL machinery. Our method features an efficient policy for generating DAGs in just a single step with an optimal quadratic complexity, fueled by a novel parametrization of DAGs that directly translates a continuous space to the space of all DAGs, bypassing the need for explicitly enforcing acyclicity constraints. This approach enables us to navigate the search space more effectively by utilizing policy gradient methods and established scoring functions. In addition, we provide compelling empirical evidence for the strong performance of ALIAS in comparison with state-of-the-arts in causal discovery over increasingly difficult experiment conditions on both synthetic and real datasets.

cs.LG↗

arXiv2024

Enabling Causal Discovery in Post-Nonlinear Models with Normalizing Flows

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.

cs.LG↗

arXiv2024

Scalable Variational Causal Discovery Unconstrained by Acyclicity

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.

cs.LG↗

arXiv2023

Robust Estimation of Causal Heteroscedastic Noise Models

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.

stat.ML↗

arXiv2023

Domain Generalisation via Risk Distribution Matching

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.

cs.LG↗

arXiv2023

Differentiable Bayesian Structure Learning with Acyclicity Assurance

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.

cs.LG↗

arXiv2023

Heteroscedastic Causal Structure Learning

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.

cs.LG↗

arXiv2022

Causal Inference via Style Transfer for Out-of-distribution Generalisation

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.

cs.CV↗

arXiv2022

Diffeomorphic Information Neural Estimation

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.

cs.LG↗

arXiv2022

Conditional Independence Testing via Latent Representation Learning

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.

cs.LG↗

arXiv2022

Efficient Classification with Counterfactual Reasoning and Active Learning

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.

cs.LG↗