2021/07/06 by Changwoo J. Lee, Zhao Tang Luo, Lee, Changwoo J. +4
Decision Sciences · Engineering · Environmental Science · Mathematics · #Asphalt Pavement Performance Evaluation #FOS: Computer and information sciences #Infrastructure Maintenance and Monitoring #Machine Learning (stat.ML) #Methodology (stat.ME) #Probabilistic and Robust Engineering Design #Soil Geostatistics and Mapping #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.2107.02510
openalex publication_date 2021/07/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Graphs have been commonly used to represent complex data structures. In\nmodels dealing with graph-structured data, multivariate parameters may not only\nexhibit sparse patterns but have structured sparsity and smoothness in the\nsense that both zero and non-zero parameters tend to cluster together. We\npropose a new prior for high-dimensional parameters with graphical relations,\nreferred to as the Tree-based Low-rank Horseshoe (T-LoHo) model, that\ngeneralizes the popular univariate Bayesian horseshoe shrinkage prior to the\nmultivariate setting to detect structured sparsity and smoothness\nsimultaneously. The T-LoHo prior can be embedded in many high-dimensional\nhierarchical models. To illustrate its utility, we apply it to regularize a\nBayesian high-dimensional regression problem where the regression coefficients\nare linked by a graph, so that the resulting clusters have flexible shapes and\nsatisfy the cluster contiguity constraint with respect to the graph. We design\nan efficient Markov chain Monte Carlo algorithm that delivers full Bayesian\ninference with uncertainty measures for model parameters such as the number of\nclusters. We offer theoretical investigations of the clustering effects and\nposterior concentration results. Finally, we illustrate the performance of the\nmodel with simulation studies and a real data application for anomaly detection\non a road network. The results indicate substantial improvements over other\ncompeting methods such as the sparse fused lasso.\n