{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/bayesian-group-latent-factor-analysis-with","title":"Bayesian group latent factor analysis with structured sparsity","arxiv_id":"1411.2698","date":"2014-11-11","proceeding":null,"authors":["Shiwen Zhao","Chuan Gao","Sayan Mukherjee","Barbara E. Engelhardt"],"abstract":"Latent factor models are the canonical statistical tool for exploratory\nanalyses of low-dimensional linear structure for an observation matrix with p\nfeatures across n samples. We develop a structured Bayesian group factor\nanalysis model that extends the factor model to multiple coupled observation\nmatrices; in the case of two observations, this reduces to a Bayesian model of\ncanonical correlation analysis. The main contribution of this work is to\ncarefully define a structured Bayesian prior that encourages both element-wise\nand column-wise shrinkage and leads to desirable behavior on high-dimensional\ndata. In particular, our model puts a structured prior on the joint factor\nloading matrix, regularizing at three levels, which enables element-wise\nsparsity and unsupervised recovery of latent factors corresponding to\nstructured variance across arbitrary subsets of the observations. In addition,\nour structured prior allows for both dense and sparse latent factors so that\ncovariation among either all features or only a subset of features can both be\nrecovered. We use fast parameter-expanded expectation-maximization for\nparameter estimation in this model. We validate our method on both simulated\ndata with substantial structure and real data, comparing against a number of\nstate-of-the-art approaches. These results illustrate useful properties of our\nmodel, including i) recovering sparse signal in the presence of dense effects;\nii) the ability to scale naturally to large numbers of observations; iii)\nflexible observation- and factor-specific regularization to recover factors\nwith a wide variety of sparsity levels and percentage of variance explained;\nand iv) tractable inference that scales to modern genomic and document data\nsizes.","url_abs":"http://arxiv.org/abs/1411.2698v2","url_pdf":"http://arxiv.org/pdf/1411.2698v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"bayesian-group-latent-factor-analysis-with","repo_url":"https://github.com/judyboon/BASS","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"parameter-estimation","task_name":"parameter estimation"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}