fit mixed graphical models

This paper addresses the challenge of modeling variable dependencies in mixed-type data—encompassing continuous, discrete, categorical, and zero-inflated count variables. We propose the first Bayesian pairwise graphical model that is both theoretically rigorous and practically robust. Methodologically, we innovatively integrate spike-and-slab priors into mixed graphical models and perform joint structure learning via conditional-likelihood-based MCMC sampling. The framework rigorously preserves both global and local Markov properties and natively accommodates missing-at-random (MAR) missingness. Experiments demonstrate substantial improvements over state-of-the-art methods across four simulated missing-data scenarios. Applied to real-world adolescent eating disorder data, our model successfully uncovers dynamic shifts in cognitive–behavioral association structures before and after treatment, revealing interpretable neurocognitive pathways underlying therapeutic change.

This paper addresses the problem of modeling discrete dynamic graphs under high-dimensional covariate-dependent dependencies. We propose a class of covariate-driven dynamic discrete graph models that capture smoothly evolving network structures among discrete random variables as functions of covariates, subsuming the dynamic Ising model as a special case. Methodologically, we introduce a pseudo-likelihood-based high-dimensional parameter estimation framework to circumvent the intractability of exact likelihood computation, and integrate a birth-death MCMC algorithm for adaptive sparse graph structure selection. Theoretically and empirically, our approach achieves both statistical consistency and computational efficiency in high-dimensional settings, substantially improving identification accuracy and inferential robustness for covariate-dependent dynamic networks. This work provides a novel paradigm for modeling conditional dependence structures in complex systems—such as neural activity and social contagion—where interactions evolve with contextual covariates.

This study addresses the challenge of modeling how external risk factors influence multivariate conditional independence structures within a unified graphical framework. To this end, the authors propose a novel class of models termed “profile graphical models,” formally defining this family for the first time and showing that both multigraphs and chain graphs arise as special cases. They further establish the compatibility of profile graphical models with the independence interpretation of two-block LWF chain graphs. Building upon a continuous spike-and-slab prior, they develop a Bayesian inference procedure for Gaussian undirected profile graphical models and devise an efficient EM algorithm for implementation. Empirical evaluations on both synthetic data and protein signaling networks in acute myeloid leukemia demonstrate that the proposed model yields more parsimonious network representations and significantly improves the capture of patient heterogeneity compared to existing approaches.

This work proposes a nonparametric Bayesian clustering approach for multivariate categorical data that explicitly incorporates graphical models to account for heterogeneous dependence structures across clusters. Unlike conventional methods that assume conditional independence of variables within each cluster, the proposed framework employs a Dirichlet process mixture of categorical graphical models to partition individuals into groups that are homogeneous not only in marginal distributions but also in their underlying dependency structures and associated parameters. Full Bayesian inference is performed via Markov chain Monte Carlo (MCMC) to enable posterior analysis. To the best of our knowledge, this is the first method to explicitly integrate graphical models into the clustering of categorical data, thereby effectively capturing inter-group differences in dependence patterns. Experiments on simulated data as well as real-world genomic and voting records demonstrate that the approach significantly outperforms existing methods that ignore such structural dependencies.

Existing causal discovery methods applied to observational data rely on strong functional assumptions—such as linearity or additive noise—to ensure structural identifiability; however, these assumptions often fail to hold in practice, undermining theoretical guarantees and empirical performance. Method: We propose a novel multivariate causal discovery framework that operates without interventional data and relaxes functional assumptions. Our approach is the first to extend Bayesian model selection to continuous causal graph learning: it employs a hyperparameterized adjacency matrix, jointly optimizes the marginal likelihood and a differentiable acyclicity regularizer, and integrates a Causal Gaussian Process Conditional Density Estimator (CGP-CDE) for Bayesian nonparametric inference. Optimization proceeds via continuous relaxation, ensuring scalability and theoretical robustness. Results: The method achieves significant improvements over state-of-the-art baselines on both synthetic and real-world benchmarks, with controllable error rates and strong generalization—breaking the traditional dependence of identifiability on either strong functional assumptions or interventional data.

This work addresses the challenges posed by the intractable normalization constant in high-dimensional, unbounded discrete graphical models, which complicates parameter constraints and conditional dependence modeling. To circumvent this issue, the authors propose a bounded discrete graphical model that inherently avoids normalization difficulties and introduce an unnormalized estimation method based on Regularized Generalized Score Matching (BRIDGE). By reparameterizing variables to restore curvature in the loss function, the approach overcomes objective degeneracy. Under non-convex settings, the method establishes a population-level separability property that substitutes for global convexity, enabling exact support recovery in high dimensions. Theoretical analysis provides non-asymptotic bounds on estimation error and guarantees graph structure consistency. Experimental results demonstrate that BRIDGE is stable, computationally efficient, and yields highly interpretable outcomes.

This study addresses the problem of identifying sets of predictive variables that remain stable under interventions in complex systems involving both latent variables and causal cycles. By extending graphical models, the work generalizes the theory of stable blankets to this broad setting for the first time: it employs acyclic directed mixed graphs (ADMGs) with m-separation to handle latent confounding, and directed graphs (DGs/DMGs) with σ-separation to represent cyclic causal structures, leveraging strongly connected components (SCCs) as fundamental building blocks of cyclic systems. The paper provides graph-theoretic characterizations of Markov blankets, stable fronts, and stable blankets, rigorously establishes necessary and sufficient conditions for conditional independence between the response variable and intervention variables given a predictor set, and proves the minimality and uniqueness of such stable predictor sets.