## Bayesian Factor Regression Models in the "Large p, Small n" Paradigm (2003)

Venue: | Bayesian Statistics |

Citations: | 120 - 14 self |

### BibTeX

@INPROCEEDINGS{West03bayesianfactor,

author = {Mike West},

title = {Bayesian Factor Regression Models in the "Large p, Small n" Paradigm},

booktitle = {Bayesian Statistics},

year = {2003},

pages = {723--732},

publisher = {Oxford University Press}

}

### Years of Citing Articles

### OpenURL

### Abstract

TOR REGRESSION MODELS 1.1 SVD Regression Begin with the linear model y = X# + # where y is the n-vector of responses, X is the n p matrix of predictors, # is the p-vector regression parameter, and # , # I) is the n-vector error term. Of key interest are cases when p >> n, when X is "long and skinny." The standard empirical factor (principal component) regression is best represented using the reduced singular-value decomposition (SVD) of X, namely X = FA where F is the nk factor matrix (columns are factors, rows are samples) and A is the k p SVD "loadings" matrix, subject to AA # = I and F # F = D where D is the diagonal matrix of k positive singular values, arranged in decreasing order. This reduced form assumes factors with zero singular values have been ignored without loss; k with equality only if all singular values are positive. Now the regression transforms via X# = F# where # = A# is the k-vector of regression parameters for the factor variables, representing

### Citations

209 | the clinical status of human breast cancer by using gene expression profiles - West, Blanchette, et al. |

99 |
Ordinal data modeling
- Johnson, Albert
- 1999
(Show Context)
Citation Context ...001) involve binary regression. A probit model is trivially constructed by treating the yi as latent and observing only indicators of yi > 0. Logistic and other variants are also standard extensions (=-=Albert and Johnson, 1999-=-, ch. 3). Our use of generalised shrinkage priors and high-dimensional predictors since 1999 is innovative, and has been used in gene expression profiling for nearly three years now (1999-2002); as re... |

64 | Bayesian Dynamic Factor Models and Portfolio Allocation
- Aguilar, West
- 2000
(Show Context)
Citation Context ... of Section 1 arises as a limiting case; this explains and justifies the design-dependency issues discussed in Section 1. Write xi for the i th column of X and consider the latent factor model (e.g., =-=Aguilar and West, 2000; Lopes and West,-=- 1999) where xi = Bλi + νi λi ∼ N(λi | 0, ∆ 2 ) and νi ∼ N(νi | 0, Ψ 2 ). (2) Here λi is a k−vector of uncertain latent factors for case i, B is a p × k factor loadings matrix paramet... |

28 | Prediction and uncertainty in the analysis of gene expression profiles - Spang, Zuzan, et al. - 2002 |

21 | The Choice of Variables in Multivariate Regression: A Non-conjugate Bayesian Decision Theory Approach - Brown, Vannucci, et al. - 1999 |

20 | Application of near infrared reflectance spectroscopy to the compositional analysis of biscuits and biscuit doughs. J Sci Food Agric - BG, Fearn, et al. - 1984 |

9 | DNA microarray data analysis and regression modeling for genetic expression profiling. Methods for gene expression analysis
- West, Nevins, et al.
- 2002
(Show Context)
Citation Context ...lications in Gene Expression Profiling Original motivation for this work comes from gene expression analysis in which predictors are genes and p may range up to 30,000. Our studies (Spang et al 2001; =-=West et al 2000-=-, 2001) involve binary regression. A probit model is trivially constructed by treating the yi as latent and observing only indicators of yi > 0. Logistic and other variants are also standard extension... |

7 |
Model uncertainty in factor analysis
- Lopes, West
- 1999
(Show Context)
Citation Context ...a limiting case; this explains and justifies the design-dependency issues discussed in Section 1. Write xi for the i th column of X and consider the latent factor model (e.g., Aguilar and West, 2000; =-=Lopes and West, 1999) where xi = Bλi -=-+ νi λi ∼ N(λi | 0, ∆ 2 ) and νi ∼ N(νi | 0, Ψ 2 ). (2) Here λi is a k−vector of uncertain latent factors for case i, B is a p × k factor loadings matrix parameter, and νi is a vector... |