The paper uses Gaussian mixture models for Bayesian networks and proposes an optimization algorithm.
problem Modeling nodes in Bayesian networks with complex distributions.
method Gaussian mixture models combined with double iteration algorithm.
result The double iteration algorithm optimizes Gaussian mixture models effectively.
A new method for fast Bayesian mixture model estimation.
problem Estimating Bayesian mixture models is computationally challenging.
method Amortized Bayesian Inference (ABI) framework for mixture models.
result The method provides fast inference for mixture models.
Bayesian approach learns nonparametric mixture components from heterogeneous data.
problem Realistic modeling of heterogeneous data populations with nonparametric mixture components.
method Bayesian nonparametric modeling using Dirichlet process mixture priors.
result Posterior contraction rates for component densities are nearly polynomial, improving over deconvolution methods.
The parsimonious Gaussian mixture models, which exploit an eigenvalue decomposition of the group covariance matrices of the Gaussian mixture, have shown their success in particular in cluster analysis. Their estimation is in general performed by maximum likelihood estimation and has also been considered from a parametr…
Posterior regularization enhances Bayesian hierarchical mixture clustering by improving node separation.
problem High nodal variance in BHMC trees, leading to weak separation between nodes at higher levels.
method Employing Posterior Regularization to impose max-margin constraints on nodes at every level.
result Improves cluster separation in BHMC models, enhancing overall model performance.
New method for summarizing Bayesian mixture models using sliced Wasserstein distances.
problem Estimating the mixing measure in nonparametric Bayesian mixture models.
method Decision-theoretic approach using sliced Wasserstein distances for Gaussian mixtures.
result Effective estimation of the mixing measure and mixture density.
Novel connections between Neyman-Scott processes and Bayesian nonparametric mixture models enable scalable inference.
problem Efficiently modeling and detecting clusters in spatiotemporal data.
method Adapting collapsed Gibbs sampling for Neyman-Scott processes via connections to mixture of finite mixture models.
result Demonstrated scalability and effectiveness on neural spike trains and document streams.
A new sampler speeds up Bayesian mixture models.
problem Sampling from Bayesian finite mixture models is slow and hard.
method Introduces a non-reversible sampling scheme for Bayesian finite mixture models.
result The new sampler outperforms classical samplers in many scenarios, especially during convergence.
Bayesian models combine experts with a flexible gating mechanism for complex data.
problem Theoretical properties of Bayesian mixture-of-experts models with softmax gating remain unexplored.
method Investigated asymptotic behavior of posterior distribution for density estimation, parameter estimation, and model selection.
result Established posterior contraction rates for density estimation and parameter estimation, providing insights for practical model design.
In binary-transaction data-mining, traditional frequent itemset mining often produces results which are not straightforward to interpret. To overcome this problem, probability models are often used to produce more compact and conclusive results, albeit with some loss of accuracy. Bayesian statistics have been widely us…
Paper proposes a VB method for TS-SBP mixture models with reduced computational cost.
problem Efficiently learning tree-structured stick-breaking process mixture models.
method Utilizes Bayes coding algorithm for context tree models to calculate sums over all possible trees.
result Proposes a learning algorithm with less computational cost for TS-SBP mixture of Gaussians.
New algorithm improves mixing in Bayesian mixture models.
problem Slow mixing in Bayesian mixture models.
method A new Monte Carlo algorithm for sampling from the marginal posterior of a general integrable mixture.
result The new algorithm achieves excellent mixing times, outperforming standard Gibbs sampling in some cases.
Bayesian model improves cure fraction estimation in survival analysis.
problem Estimating cure fraction in survival analysis.
method Hierarchical Bayesian framework for semiparametric mixture cure model.
result Improved accuracy in capturing unobserved heterogeneity.
Bayesian framework learns latent preference archetypes for many-objective optimization.
problem Expanding space of trade-offs and context-dependent human values.
method Dirichlet-process mixture model for latent preference archetypes, hybrid queries for efficient information.
result Mixture-aware Bayesian optimization outperforms standard methods on synthetic and real-world benchmarks.
New methods combine model predictions to avoid linear mixtures' limitations.
problem Combining predictions from different models to avoid linear mixtures' limitations.
method Log-linear pooling (locking) and quantum superposition (quacking) to optimise model weights.
result Demonstrated locking method with illustrative example and practical application.
In this paper, a scale mixture of Normal distributions model is developed for classification and clustering of data having outliers and missing values. The classification method, based on a mixture model, focuses on the introduction of latent variables that gives us the possibility to handle sensitivity of model to out…
Bayesian approach approximates probability functions of Gaussian mixtures.
problem Approximating probability functions of non-spherical Gaussian mixtures.
method Bayesian decomposition, spherical radial decomposition, random sampling.
result Established differentiability and integral representation of gradient for probability functions.
Survey on Bayesian inference for Gaussian mixture models.
problem Estimating parameters of Gaussian mixture models using Bayesian methods.
method Uses Bayesian inference to estimate parameters and uncertainty of Gaussian mixture models.
result Bayesian approach provides point estimates and associated uncertainty for mixture model parameters.
Bayesian model clusters brain activity time series.
problem Heterogeneous multivariate time series in brain imaging.
method Group-based Bayesian mixture of smoothing splines with covariate effects.
result Distinct brain activity patterns identified.
Improved phylogenetic inference using VBPI-Mixtures for tree topology and branch length.
problem Multimodality of tree-topology posterior distributions in phylogenetic inference.
method VBPI-Mixtures algorithm that uses mixture learning within the BBVI framework.
result VBPI-Mixtures captures tree-topology distributions better than VBPI.
Bayesian networks with hidden variables help identify causal relationships obscured by confounding.
problem Identifying causal relationships obscured by unobserved confounders.
method Use finite k-mixtures of Bayesian networks with hidden variables to recover the joint probability distribution and identify causal relationships. result First algorithm to learn mixtures of non-empty DAGs, recovering identifiable causal relationships.
SMI uses mixture models to improve SVGD's performance in Bayesian inference.
problem Variance collapse in SVGD for Bayesian inference, especially with small models.
method Generalizes SVGD to Stein mixture models, optimizing an ELBO lower bound.
result SMI avoids variance collapse and accurately estimates uncertainty for small BNNs.
Improved Bayesian analysis for SVM models using a mixture sampler.
problem Efficient simulation-based analysis of stochastic volatility in mean models.
method Developed a generalized mixture sampler for SVM models, approximating non-central chi-squared distributions as mixtures of normal distributions.
result The proposed method outperforms other volatility models based on marginal likelihoods in empirical studies.
The paper develops efficient algorithms for variational inference with mixtures of isotropic Gaussians.
problem Efficiently approximating multimodal Bayesian posteriors.
method Develops a variational framework and efficient algorithms for mixtures of isotropic Gaussians.
result The approach provides accurate approximations of multimodal Bayesian posteriors while being memory and computationally efficient.
A new method uses mixture approximations to improve diffusion models for Bayesian inverse problems.
problem Approximating posterior distributions in Bayesian inverse problems with intractable likelihoods.
method Proposes a mixture-based approximation of intermediate posterior distributions and uses Gibbs sampling for practical sampling.
result Validated the approach on image inverse problems and audio source separation, demonstrating improved performance.
A new method for density estimation using nearest neighbor Dirichlet mixtures.
problem Slow and unstable Bayesian density estimation methods.
method Nearest neighbor grouping, local Bayesian parametric models, Dirichlet prior, Monte Carlo sampling.
result Effective density estimation with improved computational efficiency.
Bayesian Optimization improves data mixture selection for large language models.
problem Optimizing the training data mixtures for large language models.
method Viewed as a black-box hyperparameter optimization problem, using Bayesian Optimization.
result Consistently strong results with speed-ups of over 500%.
Bayesian model averaging improves causal effect estimation by averaging over multiple models.
problem Estimating causal effects under linear Structural Causal Models (SCMs).
method Bayesian model averaging using Gaussian scale mixture distributions for computational efficiency.
result Bayesian model averaging is optimal for causal effect estimation.
A Bayesian filtering algorithm is developed for a class of state-space systems that can be modelled via Gaussian mixtures. In general, the exact solution to this filtering problem involves an exponential growth in the number of mixture terms and this is handled here by utilising a Gaussian mixture reduction step after …
In this paper we propose a novel framework for the construction of sparsity-inducing priors. In particular, we define such priors as a mixture of exponential power distributions with a generalized inverse Gaussian density (EP-GIG). EP-GIG is a variant of generalized hyperbolic distributions, and the special cases inclu…
Bayesian mixture models inference in federated learning
problem Inference of Bayesian mixture models in federated learning
method Consensus Monte Carlo approach
result Recovery of small clusters with greater accuracy than standard MCMC
Bayesian PROCOVA uses AI to adjust for covariates in RCTs.
problem Unbiased and precise treatment effect inferences from RCTs.
method Generative AI constructs digital twins for covariate adjustment, using an additive mixture prior.
result Efficiency gains in smaller RCTs compared to frequentist methods.
Study on Dirichlet process mixtures for clustering consistency.
problem Consistency of clustering with Dirichlet process mixtures.
method Analysis of posterior distribution as sample size increases, focusing on consistency for the number of clusters.
result Consistency for the number of clusters can be achieved with a properly adapted concentration parameter in a Bayesian setting.
Bayesian framework for analyzing heterogeneous covariance data with a novel MoE-Wishart model.
problem Analyzing complex multivariate systems with varying covariance structures.
method Comprehensive Bayesian framework using mixture-of-experts Wishart model with predictor-dependent mixture weights.
result Accurate subpopulation recovery and estimation in heterogeneous covariance scenarios.
Bayesian framework uses context trees for efficient time series modeling.
problem Building flexible and interpretable mixture models for real-valued time series.
method Hierarchical Bayesian modelling with context trees and autoregressive models.
result The methods outperform state-of-the-art techniques on simulated and real-world experiments.
HS-MoE selects sparse experts using adaptive priors and data-adaptive gating.
problem Sparse expert selection in mixture-of-experts architectures.
method Combines horseshoe prior with input-dependent gating for data-adaptive sparsity.
result Data-adaptive sparsity in expert usage.
This work relates the framework of model-based clustering for spatial functional data where the data are surfaces. We first introduce a Bayesian spatial spline regression model with mixed-effects (BSSR) for modeling spatial function data. The BSSR model is based on Nodal basis functions for spatial regression and accom…
Bayesian geoacoustic inversion improved using MDN.
problem Efficiently solving Bayesian geoacoustic inversion problems.
method Deriving geoacoustic statistics from multidimensional posterior density using MDN, training the network on the whole parameter space.
result The network provides reliable predictions and good generalization performance, solving problems in seconds.
There is a widespread need for statistical methods that can analyze high-dimensional datasets with- out imposing restrictive or opaque modeling assumptions. This paper describes a domain-general data analysis method called CrossCat. CrossCat infers multiple non-overlapping views of the data, each consisting of a subset…
This work investigates training infinite mixtures with maximum likelihood for improved uncertainty quantification.
problem Improving uncertainty quantification in neural networks.
method Investigates training infinite mixtures with maximum likelihood instead of variational inference.
result The proposed method leads to stochastic networks with increased predictive variance, improved robustness, and higher entropy on out-of-distribution data.
We propose the Bayesian bridge estimator for regularized regression and classification. Two key mixture representations for the Bayesian bridge model are developed: (1) a scale mixture of normals with respect to an alpha-stable random variable; and (2) a mixture of Bartlett--Fejer kernels (or triangle densities) with r…
VMoER improves uncertainty quantification in MoE layers for scalable foundation models.
problem Uncertainty quantification in large-scale models like MoE layers.
method Structured Bayesian approach with amortized variational inference over routing logits and temperature parameter inference.
result Improves routing stability, reduces calibration error, and increases AUROC by 12%.
This paper addresses the issue of model selection for hidden Markov models (HMMs). We generalize factorized asymptotic Bayesian inference (FAB), which has been recently developed for model selection on independent hidden variables (i.e., mixture models), for time-dependent hidden variables. As with FAB in mixture model…
Bayesian models overestimate clusters, but practical summaries can correct this.
problem Bayesian mixture models overestimate the number of clusters.
method Simulations and gene expression data analysis using MCMC summarisation.
result Overestimation is limited in finite samples and can be corrected, but misspecification leads to significant overestimation.
Study how depth affects inference in deep Bayesian neural networks.
problem Understanding how depth impacts inference in overparameterized linear Bayesian neural networks.
method Interpreting finite deep linear Bayesian neural networks as scale mixtures of Gaussian process predictors.
result Advances analytical understanding of how depth affects inference in a simple class of Bayesian neural networks.
We propose a novel "tree-averaging" model that utilizes the ensemble of classification and regression trees (CART). Each constituent tree is estimated with a subset of similar data. We treat this grouping of subsets as Bayesian ensemble trees (BET) and model them as an infinite mixture Dirichlet process. We show that B…
Bayesian approach to robust risk measures under model uncertainty.
problem Representing robust risk measures as a single probability measure.
method Introducing two types of risk measures and analyzing their relation to robust risk measures.
result Robust risk measures can be represented by a mixture probability measure, a Bayesian approach.
Study identifies components of unknown interventions in a mixture.
problem Identify components of a mixture of unknown interventions on a causal Bayesian Network.
method Construct example showing components not identifiable. Prove identifiability under mild conditions. Develop efficient algorithm for recovery. Analyze performance in simulation.
result Components of a mixture of unknown interventions can be uniquely identified under certain conditions.