Graphical classifier handles model uncertainty with Bayesian model averaging.
problem Model selection uncertainty in Bayesian classification.
method Particle Gibbs strategy for posterior sampling from decomposable graphical models.
result Proposed classifier outperforms standard Bayesian and other classifiers.
Bayesian method for estimating functional graphical models from neuroimaging data.
problem Estimating dependence structures from functional data in neuroscience.
method Fully Bayesian regularization scheme, including direct Bayesian analog of functional graphical lasso and graphical horseshoe.
result Insight into brain compensation after traumatic brain injury.
ECM algorithm estimates graphical models efficiently in high dimensions.
problem Bayesian graphical models in high-dimensional settings are computationally infeasible.
method ECM algorithm using mixture priors for posterior exploration.
result ECM approach enables fast posterior exploration and incorporates multiple sources of information.
Bayesian method selects sparse models efficiently with less bias.
problem Sparse model selection and regularization in Gaussian graphical models.
method Continuous spike-and-slab framework with EM algorithm for fast explorations.
result Efficient selection of sparse models with less bias compared to other methods.
New method improves inference for Bayesian graphical models.
problem Improving inference efficiency and accuracy for Bayesian graphical models.
method Proposes Heron inference, a deterministic method for Bayesian graphical models.
result Significantly outperforms baseline methods in inference for Bayesian graphical models.
New Bayesian method uses momentum-space renormalization for image modeling.
problem Bayesian image modeling challenges in Gaussian graphical models.
method Combines marginal likelihood maximization with momentum-space renormalization.
result Scheme for computing hyperparameters and mean square errors.
Bayesian method estimates Kronecker graphical models from autoregressive processes.
problem Estimating Kronecker graphical models from autoregressive Gaussian processes.
method Bayesian approach to estimate Kronecker graphical models.
result Effectiveness demonstrated through numerical experiments and real-world data application.
Graphical-GAN combines Bayesian networks and GANs for structured data modeling.
problem Modeling structured data with complex dependencies.
method Integrates Bayesian networks and GANs, introduces structured recognition model, and generalizes EP algorithm.
result Successfully learns discrete and temporal structures on visual datasets.
Graphical normalizing flows use Bayesian networks to improve normalizing flows' interpretability and performance.
problem Improving the interpretability and performance of normalizing flows.
method Revisiting normalizing flows as probabilistic graphical models, proposing graphical normalizing flows with either prescribed or learnable graph structures.
result Graphical conditioners lead to competitive white box density estimators.
The idea of computer vision as the Bayesian inverse problem to computer graphics has a long history and an appealing elegance, but it has proved difficult to directly implement. Instead, most vision tasks are approached via complex bottom-up processing pipelines. Here we show that it is possible to write short, simple …
Bayesian method tackles M-Bias in causal inference.
problem M-Bias causes incorrect causal effect inference when adjusting for variables.
method Bayesian approach to replicate Pearl's solution while conditioning on all variables.
result Bayesian solution to M-Bias problem is possible.
We provide a classification of graphical models according to their representation as subfamilies of exponential families. Undirected graphical models with no hidden variables are linear exponential families (LEFs), directed acyclic graphical models and chain graphs with no hidden variables, including Bayesian networks …
Bayesian networks combine prior knowledge with data to learn causal relationships.
problem Learning causal relationships from data.
method Constructing Bayesian networks from prior knowledge and using statistical methods to improve models.
result Bayesian networks can handle missing data and learn causal relationships.
One of the fundamental tasks of science is to find explainable relationships between observed phenomena. One approach to this task that has received attention in recent years is based on probabilistic graphical modelling with sparsity constraints on model structures. In this paper, we describe two new approaches to Bay…
Bayesian methods can handle causal inference without needing do-calculus.
problem The challenge of representing and addressing causal problems using probability theory.
method Bayesian statistics and probabilistic graphical models.
result Causal effects can be estimated within the standard Bayesian paradigm.
We consider the problem of learning Bayesian network classifiers that maximize the marginover a set of classification variables. We find that this problem is harder for Bayesian networks than for undirected graphical models like maximum margin Markov networks. The main difficulty is that the parameters in a Bayesian ne…
Proposes a Bayesian model for variable clustering with Gaussian graphical models to handle noise.
problem Noise in partial correlations can affect variable clustering results.
method Develops a Bayesian model that accounts for small but not zero partial correlations, evaluates using marginal likelihood.
result The proposed method is more accurate than BIC in noisy settings and provides more sensible clustering results.
The paper improves Bayesian precision matrix estimation for high-dimensional sparse data.
problem Estimating sparse precision matrices in high-dimensional settings.
method Tempered posterior with fully specified horseshoe prior.
result Concentration results and theoretical oracle inequality for posterior.
This paper uses Bayesian models to analyze CTA returns across short and long-term trends.
problem The relative merits and interactions of short- and long-term trend systems in CTA replication remain controversial.
method Dynamic decomposition of CTA returns into short-term trend, long-term trend, and market beta factors using a Bayesian graphical model.
result The blend of horizons shapes the strategy's risk-adjusted performance.
New graph model handles cycles and latent variables.
problem Models for cycles and latent variables.
method Directed graphs with hyperedges (HEDGes), Markov properties.
result Markov properties for HEDGes are not equivalent.
The aim of this chapter is twofold. In the first part we will provide a brief overview of the mathematical and statistical foundations of graphical models, along with their fundamental properties, estimation and basic inference procedures. In particular we will develop Markov networks (also known as Markov random field…
Bayesian method learns network structure from Gaussian process priors.
problem Computational infeasibility of Bayesian structure learning in GPNs.
method Monte Carlo and MCMC methods for sampling network structures.
result Method outperforms state-of-the-art algorithms in recovering network structure.
New algorithm speeds up Bayesian structure learning in Gaussian graphical models.
problem Computational bottleneck in evaluating ratios of G-Wishart normalizing constants.
method Explicit closed-form approximation of the ratio of normalizing constants within the search algorithm.
result Significant improvement in scalability of structure learning without sacrificing accuracy.
Theory of graphical models has matured over more than three decades to provide the backbone for several classes of models that are used in a myriad of applications such as genetic mapping of diseases, credit risk evaluation, reliability and computer security, etc. Despite of their generic applicability and wide adoptan…
Graphical interpretation of unfairness in causal Bayesian networks.
problem Unfairness in datasets and models.
method Causal Bayesian networks to interpret and measure unfairness.
result Causal Bayesian networks provide a tool to measure and design fair models.
New neural network approach for optimizing latent variable models.
problem Stability issues in marginalizing Gaussian Bayesian networks.
method Developed a new graphical structure and a neural network algorithm.
result Established a duality between parameter optimization and neural network training.
Bayesian method learns graph structures from Gaussian data efficiently.
problem Scalability issue in Bayesian Gaussian graphical model inference.
method Marginal pseudo-likelihood, birth-death and reversible jump MCMC algorithms.
result Efficient graph structure learning for large graphs with over 1,000 nodes.
Bayes rule replaces do-calculus for causal inference.
problem Representing and addressing causal problems with probability theory.
method Encoding causal graphical models in Probabilistic graphical models and using Bayesian statistics.
result Causal effects can be estimated entirely within the Bayesian paradigm.
Quantum models use complex Hilbert spaces for uncertainty.
problem Modeling dynamics in continuous-valued features.
method Quantum Graphical Models (QGMs) and Hilbert Space Embedding (HSE).
result HSE-HQMMs are competitive with state-of-the-art models.
sparsebn learns large Bayesian networks from high-dimensional data.
problem Learning graphical models from large, high-dimensional datasets with interventions.
method Focuses on scalability and consistency in high-dimensional settings, learning causal networks from data.
result Achieves the goal of learning a causal network from data.
Graphical models provide powerful tools to uncover complicated patterns in multivariate data and are commonly used in Bayesian statistics and machine learning. In this paper, we introduce the R package BDgraph which performs Bayesian structure learning for general undirected graphical models (decomposable and non-decom…
This paper provides efficient algorithms for computing entropy and KL divergence in Bayesian networks.
problem Computing entropy and KL divergence for Bayesian networks efficiently.
method Leveraging the graphical structure of Bayesian networks, the paper provides computationally efficient algorithms.
result Reduces computational complexity of KL divergence from cubic to quadratic for Gaussian BNs.
Paper introduces a nonparametric functional graphical model for random functions.
problem Estimating probabilistic conditional independence in functional graphical models.
method Functional sufficient dimension reduction to relax Gaussian or copula Gaussian assumptions.
result Enhances estimation accuracy and retains probabilistic conditional independence.
A graphical model is a statistical model that is associated to a graph whose nodes correspond to variables of interest. The edges of the graph reflect allowed conditional dependencies among the variables. Graphical models admit computationally convenient factorization properties and have long been a valuable tool for t…
Graphical models help infer domain adaptation across unknown distributions.
problem Unknown changes in joint distribution across domains.
method Use graphical models to encode and infer changes in data distribution.
result Automated domain adaptation framework improves posterior inference of target variable.
Bayesian method improves portfolio management with limited data.
problem Estimating covariance or precision matrix for large portfolios is challenging.
method Bayesian graphical LASSO for precision matrix estimation.
result The Bayesian approach outperforms non-Bayesian methods in stability and precision matrix estimation.
Real-time scene understanding solved using Approximate Bayesian Computation.
problem Predicting human actions, object poses, and pedestrian crossings from depth images.
method Bayesian error model, neural surrogates, and adaptive discretization.
result Real-time inference on real-world problems is feasible.
Normalizing flows are shown to be equivalent to Bayesian networks, revealing new insights.
problem Understanding the limitations and capabilities of normalizing flows.
method Revisiting normalizing flows as probabilistic graphical models and analyzing their structure.
result Normalizing flows can be reduced to Bayesian networks, revealing new insights into their structure and capabilities.
We propose a general formalism of iterated random functions with semigroup property, under which exact and approximate Bayesian posterior updates can be viewed as specific instances. A convergence theory for iterated random functions is presented. As an application of the general theory we analyze convergence behaviors…
We consider the inference of the structure of an undirected graphical model in an exact Bayesian framework. More specifically we aim at achieving the inference with close-form posteriors, avoiding any sampling step. This task would be intractable without any restriction on the considered graphs, so we limit our explora…
AutoBayes automates Bayesian graph exploration for robust machine learning.
problem Learning representations invariant to nuisance variations in machine learning.
method Automated Bayesian inference framework exploring different graphical models.
result Significant performance improvement with nuisance-invariant machine learning pipelines.
Bayesian inference of discrete component states in civil infrastructures using PGMs and GNNs.
problem Inferring discrete states of civil infrastructure components from measurable responses is an ill-posed inverse problem.
method The study proposes a novel Bayesian inversion paradigm based on Probabilistic Graphical Models (PGMs) and Graph Neural Networks (GNNs). PGMs are used to model the problem, with parameters learned from data and structural topology prior. Inference is accomplished by GNNs, and a graph property-based training strategy is developed.
result The proposed framework effectively solves the challenges of inferring the posterior PDF for discrete variables in high-dimensional problems.
Bayesian nonparametric approach for clustering non-exchangeable groups.
problem Clustering grouped data with dependencies among groups.
method Graphical Dirichlet process modeling with Markov property.
result Efficient posterior inference algorithm developed.
Study forecasts stock returns on JSE using SGDLMs capturing cross-series dependencies.
problem Accurate forecasting of multivariate time series data.
method Simultaneous Graphical Dynamic Linear Models (SGDLMs) with customised DLMs and importance sampling/mean-field variational Bayes.
result SGDLMs accurately forecast stock data on JSE and respond to market changes.
A new approach reduces computational time in Bayesian Optimisation Algorithm (BOA).
problem Time-consuming PGM updates in BOA.
method Proposes FBOA, a new BOA-based optimisation approach that avoids frequent PGM updates.
result FBOA presents competitive results while significantly saving computational time.
Develops a new multivariate regression model for complex outcomes.
problem Flexible, heterogeneous, and residual-dependent multivariate regression problems.
method MultiVCBART framework with Graphical Horseshoe priors.
result Empirically outperforms existing models on sparse, high-dimensional datasets.
Iterative Proportional Fitting (IPF), combined with EM, is commonly used as an algorithm for likelihood maximization in undirected graphical models. In this paper, we present two iterative algorithms that generalize upon IPF. The first one is for likelihood maximization in discrete chain factor graphs, which we define …
New framework models uncertainty with uncertainty variables.
problem Modeling uncertainty in state estimation and inference.
method Developed uncertainty variables, sets, and graphical models.
result Preserves independence properties and builds useful concepts.