arXiv Statistics ML
Graph-dependent shrinkage priors for Bayesian trend filtering
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arXiv Statistics ML
Oct 9
Regularized Small Area Estimation with Graph Laplacian Benchmarking priors
The paper introduces a Bayesian framework for small area estimation that jointly handles borrowing information across areas and benchmarking estimates to reliable aggregates via a new family of Benchmarking priors. These priors arise from a benchmark-constrained regularization problem and include a Benchmarking Prior without additional regularization, as well as Single and Multi-View Laplacian Benchmarking Priors that use graph Laplacians built from area similarities based on external covariates. Tailored MCMC algorithms are developed for posterior computation, and the models are evaluated through a data-based simulation and applied to estimate Average Household Size at the municipality level in Colombia in 2025, where graph-based regularization improves performance and Multi-View models yield more precise estimates.
arXiv Statistics ML
Aug 25
Learning discrete Bayesian networks with hierarchical Dirichlet shrinkage
arXiv:2509.13267v3 Announce Type: replace-cross Abstract: A discrete Bayesian network is a directed acyclic graph (DAG) consisting of categorical variables. Two popular approaches for DBN modeling in...
arXiv Machine Learning
3d ago
Time-partitioning Gaussian Process Mixture Model
The Time-partitioning Gaussian Process Mixture Model (TPGPMM) is a Bayesian nonparametric framework that identifies persistent regimes and models nonstationary dependence in time series. It uses an adaptive Pitman–Yor prior on contiguous segmentations combined with regime-specific Gaussian processes, and learns change points and hyperparameters via a split–merge Metropolis-within-Gibbs sampler. Experiments on the CBOE Volatility Index and the 10‑year U.S. Treasury yield recover regime structures aligned with major market and monetary‑policy events, while variants that estimate observation noise improve predictive accuracy but may reduce sparsity or event alignment.
arXiv Statistics ML
Aug 28
A Two-step Metropolis Hastings Method for Bayesian Empirical Likelihood Computation with Application to Quantile Regression and Bayesian Model Selection
The paper introduces a two-step Metropolis–Hastings algorithm designed to efficiently sample from Bayesian empirical likelihood (BayesEL) posterior distributions, addressing challenges posed by the complex, often non‑convex support of empirical likelihood. The method leverages current parameter values and estimating equations to propose new values for remaining parameters, making it suitable for problems with discontinuous estimating equations such as simultaneous quantile regression. Additionally, the approach extends naturally to BayesEL model selection via reversible‑jump MCMC, and the authors demonstrate its utility through several real‑life applications.
arXiv Machine Learning
Jul 30
Breaking the Curse with BAND: Nonparametric Distribution Estimation in High Dimensions
arXiv:2607. 26955v1 Announce Type: cross Abstract: Minimax-optimal rates for multivariate distribution estimation are known to suffer from the curse of dimensionality.
arXiv Machine Learning
Jun 3
Bayesian Tensor Decomposition with Diffusion Model Prior
arXiv:2606. 03212v1 Announce Type: new Abstract: Low-rank tensor decomposition (TD) is usually effective on clean, fully observed data, but it often degrades under severe missingness or noise.