Robust bilinear factor analysis based on the matrix-variate t distribution
CoRR(2024)
摘要
Factor Analysis based on multivariate t distribution (tfa) is a useful
robust tool for extracting common factors on heavy-tailed or contaminated data.
However, tfa is only applicable to vector data. When tfa is applied to
matrix data, it is common to first vectorize the matrix observations. This
introduces two challenges for tfa: (i) the inherent matrix structure of the
data is broken, and (ii) robustness may be lost, as vectorized matrix data
typically results in a high data dimension, which could easily lead to the
breakdown of tfa. To address these issues, starting from the intrinsic matrix
structure of matrix data, a novel robust factor analysis model, namely bilinear
factor analysis built on the matrix-variate t distribution (tbfa), is
proposed in this paper. The novelty is that it is capable to simultaneously
extract common factors for both row and column variables of interest on
heavy-tailed or contaminated matrix data. Two efficient algorithms for maximum
likelihood estimation of tbfa are developed. Closed-form expression for the
Fisher information matrix to calculate the accuracy of parameter estimates are
derived. Empirical studies are conducted to understand the proposed tbfa
model and compare with related competitors. The results demonstrate the
superiority and practicality of tbfa. Importantly, tbfa exhibits a
significantly higher breakdown point than tfa, making it more suitable for
matrix data.
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