Interpretable Heterogeneous Instrumented Principal Component Analysis

Instrumented principal component analysis (IPCA) is an important category of PCA that is anchored to a set of instruments (e.g., treatments). However, standard IPCA neither supports heterogeneity nor extracts interpretable factors. To solve these problems, we propose a novel interpretable heterogeneous IPCA (HeterIPCA). It constructs the factor loadings with rich heterogeneity by a structured graph convolutional network (SGCN), achieves a nonasymptotic bound of parameter estimation, and establishes asymptotic normality of inference. Experimental results show that HeterIPCA achieves state-of-the-art performance on various evaluation metrics. This finding may shed new light on the interpretability and heterogeneity of PCA and factor analysis.