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In this paper, we propose a probabilistic model for computing aninterpolative decomposition (ID) in which each column of the observed matrixhas its own priority or importance, so that the end result of the decompositionfinds a set of features that are representative of the entire set of features,and the selected features also have higher priority than others. This approachis commonly used for low-rank approximation, feature selection, and extractinghidden patterns in data, where the matrix factors are latent variablesassociated with each data dimension. Gibbs sampling for Bayesian inference isapplied to carry out the optimization. We evaluate the proposed models onreal-world datasets, including ten Chinese A-share stocks, and demonstrate thatthe proposed Bayesian ID algorithm with intervention (IID) produces comparablereconstructive errors to existing Bayesian ID algorithms while selectingfeatures with higher scores or priority.

Feature Selection via the Intervened Interpolative Decomposition and its Application in Diversifying Quantitative Strategies