Open research questions in Bayesian Modeling and Causal Inference
47 unresolved questions extracted from the limitations and future-work sections of 314 Bayesian Modeling and Causal Inference papers in our library. Each links back to the study that raised it.
What the literature leaves open
Future research directions include scalable causal discovery, multi-modal data integration, and regulatory pathways for causal graph neural networks. The development of more efficient and effective methods for causal inference and counterfactual reasoning is needed. The application of causal graph neural networks to other domains, such as education and social policy, is a potential area of future research.
The gap in existing healthcare AI systems is their brittleness and lack of reliability when deployed across institutions. The gap in causal machine learning is the need for more rigorous evidentiary support and validation challenges beyond standard cross-validation.
These results are limited, but they suggest AI sequence models are already good enough to offer competing explanations at well-studied genome locations, if we use them carefully.
Genetic fine-mapping identifies causal variants within trait-associated loci, but linkage disequilibrium (LD) and wide datasets complicate this sparse variable-selection problem.
Additive separability removes the hidden interaction degree of freedom, but observational residual summaries remain insufficient.
Operationalising Relative Causal Knowledge: Backbone Identifiability from Private Reports on a Shared Outcome · 2026orderMCMC and partitionMCMC were not practical under a fully connected input graph, and BCDAG failed to recover nearly all key edges under uninformative graphs, indicating methodological constraints in comparison approaches.
Approximate Bayesian inference of directed acyclic graphs in biology with flexible priors on edge states · 2026 · DOIThe paper establishes consistency under Assumption A2 (requiring ‖μ̂_a − μ_a‖_{P,1} = o_P(1)) but does not provide sufficient conditions on the causal model class or data-generating process that guarantee this assumption holds in practice.
The bounds in equation (A.6) scale with terms involving max_a ‖μ̂_a − μ_a‖_{P,1} and max_a ‖μ̂_a − μ_a‖_∞^{α+1}, but no concrete rates are provided for these nuisance parameter errors under specific structural assumptions (e.g., linear regression, propensity score models); the interplay between nuisance estimation rates and final clustering rates remains unquantified.
The lack of formal assistance in constructing Bayesian networks from scenario models. The need for a method to transfer spatio-temporal constraints from scenario models to Bayesian models.
Future research can focus on improving the accuracy and efficiency of the proposed framework. Future research can explore the application of the framework to various fields, such as economics and biology.
Traditional methods for causal discovery often falter due to restrictive linear assumptions or uninformative conditional independence tests. There is a need for a new paradigm that can address the challenges of causal discovery in complex systems.
Emerging directions, including high-dimensional causal inference and generative artificial intelligence. The potential of causal machine learning to expand the methodological tool kit available to sociologists.
The need for a deductive-inductive framework for causal machine learning in sociological research. The lack of a systematic review of recent sociological research on causal machine learning.
Future research can focus on further improving the scalability of BN structure learning. Future research can explore the application of the proposed method in different fields.
Memory-efficient exact bayesian network structure learning: a single-pass level-wise dynamic program · 2026 · DOIThe gap is that existing dynamic programming methods have large memory requirements and reliance on disk I/O. The gap is that existing structure learning methods are not efficient and scalable.
Memory-efficient exact bayesian network structure learning: a single-pass level-wise dynamic program · 2026 · DOISelf-reports are inadequate measures of self-schemas. Prior studies have not been able to verify that behavioral tasks capture distinct information from self-report.
Future research should investigate the use of personalized treatment hierarchies in other diseases and treatments. The development of new methods for creating personalized treatment hierarchies from IPD NMA models that include TCIs is needed.
The gap in the current literature is the lack of personalized treatment hierarchies in Bayesian network meta-analysis. The current methods for creating treatment hierarchies do not account for individual patient characteristics.
Existing methods and available R packages primarily focus on a single diagnostic test. Greater efficiency can be achieved by modeling multiple diagnostic tests together.
The need for efficient computation of causal effects in relational domains. The lack of a method to handle partial causal knowledge in lifted causal inference.
The exponential growth of CPT parameters with the number of parent nodes is a limitation of BN models. The curse of dimensionality affects traditional CPT parameterization.
Enhancing Bayesian networks through logistic regression: A case study of Czech Society Divisions · 2026 · DOIIn this paper, we have proposed an extension to BN learning that incorporates structured CPTs representations based on multinomial logistic regression (MLR) and ordinal logistic regression (OLR) as alternatives to standard general CPTs. Through empirical evaluation using real data from a comprehensive opinion survey, we have demonstrated that these structured representations frequently achieve superior model fit compared to general CPTs when assessed using the Bayesian Information Criterion (BIC). The proposed approach yields BNs with substantially fewer parameters while maintaining comparable predictive performance, effectively addressing the curse of dimensionality that affects traditional CPT parameterization. Our model analysis has some limitations. In the model, we omitted all demographic variables; some of them may explain certain relationships as a common explanation or a common cause for variables connected by an edge. The relationships are simplified to the most relevant variables; the less relevant ones might be included if an integrated structural learning algorithm were used. Our future work will focus on developing an integrated structural learning algorithm that simultaneously optimizes both the network structure and the CPT representations, rather than treating these as separate sequential steps. Additionally, the framework can be extended to incorporate other types of local CPT structures, including Noisy-MIN and Noisy-MAX models, as well as Noisy-Threshold models and Generalized additive models (GAMs), which are a natural generalization of the OLR models. Such extensions would provide practitioners with a comprehensive toolkit for learning parsimonious yet expressive BN models from complex real-world data. ACKNOWLEDGEMENT I would like to thank the reviewers for their constructive comments, which have helped improve the readability and clarity of the paper. This work was supported by the European Regional Development Fund project ”Beyond Security: Role of Conflict in Resilience-Building” (reg. no.: CZ.02.01.01/00/22 008/0004595). (Received July 15, 2025) R E F E R E N C E S A. Agresti: Categorical Data Analysis. Third edition. John Wiley and Sons, Hoboken, NJ 2013. M. Bucht´ık: R˚uzn´a vypr´avˇen´ı o jedn´e spoleˇcnosti. Friedrich–Ebert–Stiftung and Masarykova demokratick´a akademie, Praha 2023. 420 J. VOMLEL J. Cussens: Bayesian network learning with cutting planes. In: Proc. 27th Conference on Uncertainty in Artificial Intelligence, (F. Cozman and A. Pfeffer, eds.), AUAI Press, Corvallis 2011, pp. 153–160. DOI:10.5771/9780810873834-153 C. P. de Campos, M. Scanagatta, G. Corani, and M. Zaffalon: Entropy-based pruning for learning Bayesian networks using BIC. Artificial Intelligence 260 (2018), 42–50. DOI:10.1016/j.artint.2018.04.002 F. J. D´ıez and S. F. Gal´an: An efficient factorization for the noisy MAX. Int. J. Intell. Systems 18 (2003), 165–177. DOI:10.1002/int.10080 S. Epskamp, A. O. J. Cramer, L. J. Waldorp, V. D. Schmittmann, and D. Borsboom: Network visualizations of relationships in psychometric data. J. Statist. Software 48 (2012), 4, 1–18. http://www.jstatsoft.org/v48/i04/ T. M. J. Fruchterman and E. M. Reingold: Graph drawing by force-directed placement. Software: Practice Experience 21 (1991), 11, 1129–1164. DOI:10.1002/spe.4380211102 S. Holm: A simple sequentially rejective multiple test procedure. Scand. J. Statist. 6 (1979), 65–70. http://www.jstor.org/stable/4615733 F. V. Jensen and T. D. Nielsen: Bayesian Networks and Decision Graphs. Second edition. Information Science and Statistics, Springer New York, NY 2007. DOI:10.1007/978-0-387- 68282-2 D. Koller and N. Friedman: Probabilistic Graphical Models: Principles and Techniques. The MIT Press, 2009. J. Pearl: Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann Publishers Inc., San Francisco 1988. F. Rijmen: Bayesian networks with a logistic regression model for the conditional probabilities. Int. J. Approx. Reasoning 48 (2008), 2, 659–666. In memory of Philippe Smets 1938–2005. DOI:10.1016/j.ijar.2008.01.001 G. Schwarz: Estimating the dimension of a model. Ann. Statist. 6 (1978), 2, 461–464. http://www.jstor.org/stable/2958889 C. Sharma, Z. A. Liao, J. Cussens, and P. van Beek: A score-and-search approach to learning Bayesian networks with noisy-or relations. In: Pro. 10th International Conference on Probabilistic Graphical Models (PGM 2020). Proc. Machine Learning Research 138 (2020), pp. 413–42. https://proceedings.mlr.press/v138/sharma20a.html J. Vomlel, V. Kratochv´ıl,and F.
Enhancing Bayesian networks through logistic regression: A case study of Czech Society Divisions · 2026 · DOIConcept drift threatens the validity of structural causal models estimated on non-stationary time series. Recent neuro-symbolic pipelines like AEDL assume a fixed causal graph and static anchor set.
DriftGuard-AEDL: Concept-Drift-Aware Continual Neuro-Symbolic Causal Inference for Evolving Time Series · 2026 · DOIUsing a large simulation study, we found in our previous work [Scutari in J Mach Learn Res (Proc Track PGM 2016) 52:438–448, 2016] that the Bayesian–Dirichlet sparse (BDs) score seems to provide better accuracy in structure learning; in this paper we further show that BDs does not suffer from the issues above, and we recommend to use it for sparse data instead of BDeu.
We will use this connection to show that BDeu should not be used for structure learning from sparse data, since it violates the maximum relative entropy principle; and that it is also problematic from a more classic Bayesian model selection perspective, because it produces Bayes factors that are sensitive to the value of its only hyperparameter.
Most-cited papers in Bayesian Modeling and Causal Inference
- Guidelines for a graph‐theoretic implementation of structural equation modeling · Ecosphere · 2012 · 495 citations
- Theory-based causal induction. · Psychological Review · 2009 · 222 citations
- Bayesian Estimation for Gaussian Graphical Models: Structure Learning, Predictability, and Network Comparisons · Multivariate Behavioral Research · 2021 · 77 citations
- Exponential-Family Models of Random Graphs: Inference in Finite, Super and Infinite Population Scenarios · Statistical Science · 2020 · 70 citations
- Graphical Models for Causation, and the Identification Problem · Evaluation Review · 2004 · 62 citations
- Bayesian network models for incomplete and dynamic data · Statistica Neerlandica · 2020 · 39 citations
- Invariance, Causality and Robustness · Statistical Science · 2020 · 39 citations
- Dirichlet Bayesian network scores and the maximum relative entropy principle · Behaviormetrika · 2018 · 38 citations
- Meta-analytic Gaussian Network Aggregation · Psychometrika · 2021 · 35 citations
- Bayesian Network Models for Local Dependence Among Observable Outcome Variables · Journal of Educational and Behavioral Statistics · 2009 · 28 citations
Most recent work
- Causal Machine Learning: A Deductive–Inductive Framework for Sociological Research · KZfSS Kölner Zeitschrift für Soziologie und Sozialpsychologie · 2026
- New causal discovery algorithm over censored variables identifies subtype-specific drivers of breast cancer progression · GigaScience · 2026
- COREX: Causal Origin Resolution and Empirical eXamination — An Autonomous Multi-Stage Framework for Robust Causal Discrimination in Data-Driven AI Systems · Zenodo (CERN European Organization for Nuclear Research) · 2026
- Approximate Bayesian inference of directed acyclic graphs in biology with flexible priors on edge states · PLoS Computational Biology · 2026
- Causal K-means clustering · Journal of the Royal Statistical Society Series B: Statistical Methodology · 2026
- Time Series Causal Discovery Based on Data Augmentation and Causal Validation · SAE technical papers on CD-ROM/SAE technical paper series · 2026
- Bayesian Network Structure Learning: The New Calibrated Minimum Uncertainty Criterion and a Statistical Error Estimation Framework · bioRxiv · 2026
- Bayesian structure learning in closed skew-normal graphical models · Journal of Statistical Computation and Simulation · 2026
- Scenario-based Bayesian networks for legal evidence · Artificial Intelligence and Law · 2026
- Causal discovery in multivariate time series through mutual information featurization · International Journal of Forecasting · 2026
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