| dc.identifier.uri | http://hdl.handle.net/11401/76382 | |
| dc.description.sponsorship | This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree. | en_US |
| dc.format | Monograph | |
| dc.format.medium | Electronic Resource | en_US |
| dc.language.iso | en_US | |
| dc.publisher | The Graduate School, Stony Brook University: Stony Brook, NY. | |
| dc.type | Dissertation | |
| dcterms.abstract | Learning and visualizing complex causal or dependence structure among various variables is of great interest in applied science. Probabilistic Graphical Models, including Bayesian Networks and Markov Random Field, are well-developed tools for such problems, particularly when variables are either all categorical or continuous. In the first and major part of this text, we proposed a novel graphical structure learning approach, the MIxed Sparse FActor Network (MISFAN), to accommodate categorical and continuous variables seamlessly in one sparse Probit latent factor model. Such a network bridges the gap among latent variable models, traditional multivariate analysis and graphical models, can visualize the underlying interaction and clustering in a more extensive and succinct way, and simultaneously presents certain causal hypothesis as in a Bayesian Network, along with local conditional dependence structure as in a Markov Random Field. Another independent application of latent variable models is from the Error-in-Variable (EIV) perspective. EIV considers the intrinsic and mostly inevitable measurement error affecting the latent true predictors of a regression model. Although proved to be inconsistent and biased on data with measurement error, Ordinary Least Square still dominates for its simple computation and interpretation, while the EIV models seem to be daunting and confusing for its diverse formulations. We intend to give a clear, systematic and unified description with novel geometric insight for the common EIV models in the second part of the text. Additionally, model caveats, parameter specification and alternative estimation approaches are discussed for practical interests. | |
| dcterms.available | 2017-09-20T16:50:08Z | |
| dcterms.contributor | Zhu, Wei | en_US |
| dcterms.contributor | Wu, Song | en_US |
| dcterms.contributor | Wang, Xuefeng | en_US |
| dcterms.contributor | Yang, Yuanyuan. | en_US |
| dcterms.creator | Wen, Ruofeng | |
| dcterms.dateAccepted | 2017-09-20T16:50:08Z | |
| dcterms.dateSubmitted | 2017-09-20T16:50:08Z | |
| dcterms.description | Department of Applied Mathematics and Statistics. | en_US |
| dcterms.extent | 74 pg. | en_US |
| dcterms.format | Monograph | |
| dcterms.format | Application/PDF | en_US |
| dcterms.identifier | http://hdl.handle.net/11401/76382 | |
| dcterms.issued | 2015-12-01 | |
| dcterms.language | en_US | |
| dcterms.provenance | Made available in DSpace on 2017-09-20T16:50:08Z (GMT). No. of bitstreams: 1
Wen_grad.sunysb_0771E_12325.pdf: 1341941 bytes, checksum: 5ca2a6d56ebdc1bb62c73779b03f9cd1 (MD5)
Previous issue date: 1 | en |
| dcterms.publisher | The Graduate School, Stony Brook University: Stony Brook, NY. | |
| dcterms.subject | Statistics | |
| dcterms.subject | Conditional Dependence, Error-in-Variables, Graphical Model, Mixed Network, Probit Factor Model | |
| dcterms.title | Learning Mixed Sparse Factor Networks Structure: a Latent Variable Approach | |
| dcterms.type | Dissertation | |
