Model Averaging and Dimension Selection for the Singular Value Decomposition

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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 paper we suggest a model-based alternative to the above approach by providing prior distributions and posterior estimation for the rank of M and the components of its singular value decomposition.

key words: Carlson’s hypergeometric function, directional data, factor analysis, interaction, model selection, relational data, social network, Steifel manifold


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