Class-Distributed Learning for Multinomial Logistic Regression with High Dimensional Features and a Large Number of Classes
针对高维特征和大类别数的多项逻辑回归模型，提出一种结合降维和循环结构工作模型的类别分布式学习算法，兼顾计算效率和统计效率，并给出渐近理论和数值实验支持。
Estimating a high-dimensional multinomial logistic regression model with a larger number of categories is of fundamental importance but it presents two challenges. Computationally, it leads to heavy computation cost. Statistically, it suffers unsatisfactory statistical efficiency. Therefore, how to solve this problem in a computationally and statistically efficient way is of great interest. To tackle these challenges, we have developed a new class-distributed learning algorithm with a rank-reducible coefficient structure. The key innovation here is piecing together two important techniques for distributed computing and improved statistical efficiency. The two techniques are, respectively, dimension reduction and a circular-structured working model. Dimension reduction effectively alleviates the curse of dimensionality due to high dimensional features. A circular-structured working model allows the use of a class-distributed algorithm for distributed computing. To support our new methodology, we develop rigorous asymptotic theory and present extensive numerical experiments.