Optimal vintage factor analysis with deflation varimax
Vintage factor analysis is one important type of factor analysis that aims to first 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 to date mainly because varimax rotation requires to solve a non-convex optimization over the set of orthogonal matrices. In this paper, we propose a deflation varimax procedure that solves each row of an orthogonal matrix sequentially. In addition to its net computational gain and flexibility, we are able to fully establish theoretical guarantees for the proposed procedure in a broader context. Adopting this new deflation varimax as the second step after PCA, we further analyze this two step procedure under a general class of factor models. Our results show that it estimates the factor loading matrix in the minimax optimal rate when the signal-to-noise-ratio (SNR) is moderate or large. In the low SNR regime, we offer possible improvement over using PCA and the deflation varimax when the additive noise under the factor model is structured. The modified procedure is shown to be minimax optimal in all SNR regimes. Our theory is valid for finite sample and allows the number of the latent factors to grow with the sample size as well as the ambient dimension to grow with, or even exceed, the sample size. Extensive simulation and real data analysis further corroborate our theoretical findings.
Code (1)
Methods 이 논문이 사용한 방법론
Similar Papers 제목 키워드 기반
Deflation-Free Optimal Scoring
Sparse Optimal Scoring (SOS) reformulates linear discriminant analysis to enable feature selection through elastic net regularization, making it well-suited for high-dimensional settings where the number of features exce…
Optimizing Orthogonalized Tensor Deflation via Random Tensor Theory
This paper tackles the problem of recovering a low-rank signal tensor with possibly correlated components from a random noisy tensor, or so-called spiked tensor model. When the underlying components are orthogonal, they …
Simplifying deflation for non-convex optimization with applications in Bayesian inference and topology optimization
Non-convex optimization problems have multiple local optimal solutions. Non-convex optimization problems are commonly found in numerous applications. One of the methods recently proposed to efficiently explore multiple l…
Bayesian InferenceCore-Intermediate-Peripheral Index: Factor Analysis of Neighborhood and Shortest Paths-based Centrality Metrics
We perform factor analysis on the raw data of the four major neighborhood and shortest paths-based centrality metrics (Degree, Eigenvector, Betweeenness and Closeness) and propose a novel quantitative measure called the …
MACROCAST: A Vintage-Consistent Time Series Foundation Model for Real-Time Macroeconomic Forecasting
We introduce MACROCAST, a lightweight Time Series Foundation Model (TSFM) for real-time macroeconomic forecasting. Existing TSFMs suffer from data leakage in two forms: temporal contamination, as the model may have seen …