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Covariate Dependent Mixture of Bayesian Networks

Published 10 Jan 2025 in stat.ML and cs.LG | (2501.05745v1)

Abstract: Learning the structure of Bayesian networks from data provides insights into underlying processes and the causal relationships that generate the data, but its usefulness depends on the homogeneity of the data population, a condition often violated in real-world applications. In such cases, using a single network structure for inference can be misleading, as it may not capture sub-population differences. To address this, we propose a novel approach of modelling a mixture of Bayesian networks where component probabilities depend on individual characteristics. Our method identifies both network structures and demographic predictors of sub-population membership, aiding personalised interventions. We evaluate our method through simulations and a youth mental health case study, demonstrating its potential to improve tailored interventions in health, education, and social policy.

Summary

  • The paper introduces a novel method, Covariate Dependent Mixture of Bayesian Networks, designed to model data heterogeneity by making mixture component probabilities contingent on individual characteristics.
  • This fully probabilistic approach utilizes a Markov chain Monte Carlo (MCMC) method, specifically block Gibbs sampling, for posterior inference and uncertainty quantification, allowing identification of multiple network structures within subpopulations.
  • Evaluations on synthetic and real youth mental health data demonstrate superior performance in network structure identification compared to traditional methods, highlighting its potential for tailored interventions based on distinct causal pathways.

Covariate Dependent Mixture of Bayesian Networks

The paper "Covariate Dependent Mixture of Bayesian Networks" presents a novel methodological advancement in the area of probabilistic graphical models, specifically focusing on Bayesian Networks (BNs). The core proposition of the paper addresses the challenge of data heterogeneity in real-world applications where the assumption of homogeneity may not hold. The authors propose utilizing a mixture of Bayesian networks where the mixture component probabilities are contingent on individual covariates.

The methodology set forth allows for the identification of multiple plausible network structures that could exist within sub-populations of a given data set. The method differentiates itself by being fully probabilistic, which not only aids in uncovering these structures but also allows for subsequent Bayesian inference. By modelling components whose probabilities are parameterized by individual characteristics, the approach maintains computational tractability while asserting relevance to practical applications in health, education, and social policy.

The evaluation through simulations and case studies involves both synthetic data and real-world datasets focused on youth mental health. The proposed framework demonstrates potential for identifying network structures that would be less evident when assuming homogeneous data generating processes. Numerical results suggest that when the data stems from heterogeneous processes, the new methodology achieves superior performance in network structure identification compared to traditional approaches that assume uniformity.

Notably, the paper discusses the inference of these networks using a Markov chain Monte Carlo (MCMC) method, specifically a block Gibbs sampling scheme, to obtain samples from the posterior distribution. This is essential for both performing inference and uncertainty quantification, which are critical for data-driven decision-making.

In examining the effectiveness and robustness of the proposed method, the paper navigates multiple simulation scenarios, stressing its ability to capture distinct network structures where other methods might overlook such variations due to their reliance on a singular underlying model assumption.

When applied to the field of mental health, the methodology demonstrates its utility in clarifying complex interdependent variables. For example, in a dataset of youth mental health, the methodology can identify unique causal pathways that suggest tailored potential interventions for different population segments. For instance, anxiety's role in mental health diagnostics and its broader implications on depression and insomnia are made apparent through distinct network structures. This illustrates the practical relevance and application potential in making precise intervention decisions based on distinct causal processes.

In summary, this research contributes to significant advancements in the field of Bayesian networks by allowing researchers and practitioners to consider sub-population variation in their analyses, leading to potentially more effective and precise interventions. It opens up avenues for more granularly tailored decision-making processes in domains like mental health, driven by sophisticated modelling of heterogeneous data-generating processes. Future work could explore integrating more dynamic forms of individual covariates and expanding the models to encompass further complexities inherent in real-world data.

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