Independent Nonlinear Component Analysis

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