B1552
Title: Optimal vintage factor analysis with deflation varimax
Authors: Xin Bing - University of Toronto (Canada) [presenting]
Abstract: Vintage factor analysis is one important type of factor analysis that aims first to find a low-dimensional representation of the original data and then to seek a rotation such that the rotated low-dimensional representation is scientifically meaningful. The most widely used vintage factor analysis is the principal component analysis (PCA), followed by the varimax rotation. Despite its popularity, little theoretical guarantee can be provided mainly because varimax rotation requires solving a non-convex optimization over the set of orthogonal matrices. A deflation varimax procedure is proposed that solves each row of an orthogonal matrix sequentially. In addition to its net computational gain and flexibility, theoretical guarantees are fully established for the proposed procedure in a broad context. Adopting the new varimax approach as the second step after PCA, the two-step procedure is further analyzed under a general class of factor models. The results show that it estimates the factor loading matrix at the optimal rate when the signal-to-noise ratio (SNR) is moderate or large. In the low SNR regime, a possible improvement is offered over using PCA and the deflation procedure when the additive noise under the factor model is structured. The modified procedure is shown to be optimal in all SNR regimes.
