  In this paper, we propose a probabilistic model for computing an
interpolative decomposition (ID) in which each column of the observed matrix
has its own priority or importance, so that the end result of the decomposition
finds a set of features that are representative of the entire set of features,
and the selected features also have higher priority than others. This approach
is commonly used for low-rank approximation, feature selection, and extracting
hidden patterns in data, where the matrix factors are latent variables
associated with each data dimension. Gibbs sampling for Bayesian inference is
applied to carry out the optimization. We evaluate the proposed models on
real-world datasets, including ten Chinese A-share stocks, and demonstrate that
the proposed Bayesian ID algorithm with intervention (IID) produces comparable
reconstructive errors to existing Bayesian ID algorithms while selecting
features with higher scores or priority.
