Robust high dimensional factor models with applications to statistical machine learning.

Area of Science:

• Statistics
• Machine Learning
• Data Science

Background:

• Factor models are essential for analyzing dependent measurements across genomics, neuroscience, economics, and finance.
• Modern large-scale data present challenges like high dimensionality, strong variable dependence, heavy tails, and heterogeneity.
• High-dimensional robust factor analysis provides a robust framework to address these data complexities.

Purpose of the Study:

• To provide a selective overview of recent advancements in high-dimensional factor models.
• To explore the application of these models in statistical methods like Factor-Adjusted Robust Model selection (FarmSelect) and Factor-Adjusted Robust Multiple testing (FarmTest).
• To demonstrate the adaptability of classical methods, particularly Principal Component Analysis (PCA), to contemporary statistical challenges.

Main Methods:

• Reviewing recent advances in high-dimensional factor models.
• Highlighting the role of Principal Component Analysis (PCA) and its connections to matrix perturbation theory, robust statistics, and random projection.
• Illustrating applications of these methods in statistical estimation and inference.

Main Results:

• Classical methods like PCA can be effectively adapted for modern high-dimensional data problems.
• Factor models offer powerful tools for statistical estimation and inference, particularly in robust model selection and multiple testing.
• Connections are established between factor models and statistical learning problems such as network analysis and low-rank matrix recovery.

Conclusions:

• High-dimensional robust factor analysis is a key toolkit for tackling modern data challenges.
• Principal Component Analysis (PCA) remains a versatile and powerful tool when adapted for complex statistical problems.
• Factor models provide a unifying framework with broad applications in statistics and machine learning.