Independent Nonlinear Component Analysis

The idea of summarizing the information contained in a large number of variables by a small number of “factors” or “principal components” has been broadly adopted in statistics. This article introduces a generalization of the widely used principal component analysis (PCA) to nonlinear settings, thus providing a new tool for dimension reduction and exploratory data analysis or representation. The distinguishing features of the method include (i) the ability to always deliver truly independent (instead of merely uncorrelated) factors; (ii) the use of optimal transport theory and Brenier maps to obtain a robust and efficient computational algorithm; (iii) the use of a new multivariate additive entropy decomposition to determine the most informative principal nonlinear components, and (iv) formally nesting PCA as a special case for linear Gaussian factor models. We illustrate the method’s effectiveness in an application to excess bond returns prediction from a large number of macro factors. Supplementary materials for this article are available online.

通过少量‘因子’或‘主成分’概括海量变量所蕴含的信息这一思路，已在统计学领域得到广泛应用。本文将广泛使用的主成分分析（Principal Component Analysis，PCA）推广至非线性场景，从而为降维、探索性数据分析与数据表征提供了全新的分析工具。该方法的显著特征包括：(i) 能够始终生成真正独立（而非仅互不相关）的因子；(ii) 借助最优传输理论与布雷耶映射（Brenier maps）构建鲁棒高效的计算算法；(iii) 采用全新的多元加性熵分解方法，筛选出信息量最优的主非线性成分；(iv) 可形式上将主成分分析嵌套为线性高斯因子模型的特殊情形。我们通过将该方法应用于基于大量宏观因子的债券超额收益预测任务，验证了其有效性。本文补充材料可在线获取。