Model Averaging and Dimension Selection for the Singular Value Decomposition

By Peter D. Hoff. 2006

108 citations recorded by the source corpus.

Many multivariate data-analysis techniques for an m × n matrix Y are related to the model Y = M + E, where Y is an m × n matrix of full rank and M is an unobserved mean matrix of rank K < (m ∧ n). Typically the rank of M is estimated in a heuristic way and then the least-squares estimate of M is obtained via the singular value decomposition of Y, yielding an estimate that can have a very high variance. In this article we suggest a model-based alternative to the preceding approach by providing prior distributions and posterior estimation for the rank of M and the components of its singular value decomposition. In addition to providing more accurate inference, such an approach has the advantage of being extendable to more general data-analysis situations, such as inference in the presence of missing data and estimation in a generalized linear modeling framework.

Subfields: Analytical Chemistry, Environmental Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/66183cf3538e1aed900d424ebf9961a3d67b21e2

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Citations in the corpus

Bayesian exponential family projections for coupled data sources (2010, methodology): “The approach is similar to how Hoff (2007) made inference for binary PCA.”
The Optimal Hard Threshold for Singular Values is $4/\sqrt {3}$ (2014, methodology): “Extensive literature has formed on methods to estimate r: we point to the early [9], [10] (in Factor Analysis and Principal Component Analysis), the recent [11]–[13] (in our setting of Singular Value Decomposition), and reference therein.”
A Sparse Singular Value Decomposition Method for High-Dimensional Data (2014, background): “Proposals for rank estimation are the subject of a literature with a long history, of which we only cite Wold (1978), Gabriel (2002), and Hoff (2007).”
Hypothesis Tests for Principal Component Analysis When Variables are Standardized (2019, methodology): “…plot (Cattell 1966), resampling methods (Peres-Neto et al. 2005), cross-validation methods (Bro et al. 2008; Josse and Husson 2011), Bayesian procedures (Hoff 2007; Perez-Elizalde et al. 2012; Sobczyk et al. 2017) and statistical tests (Muirhead 1982, p. 409; Johnstone 2001; Choi et al. 2017).”