A0943
Title: Identifying interpretable latent structures in factor analysis
Authors: Maoran Xu - Duke University (United States) [presenting]
Abstract: Factor models have been widely used to summarize the variability of high-dimensional data through a set of factors with much lower dimensions. Gaussian linear factor models have been particularly popular due to their interpretability and ease of computation. However, many real data violate the multivariate Gaussian assumption. To characterize higher-order dependence and non-linearity, models that include factors as predictors in flexible multivariate regression are popular, with GP-LVMs using Gaussian process (GP) priors for the regression function and VAEs using deep neural networks. Unfortunately, such approaches lack identifiability and interpretability, and tend to produce brittle and non-reproducible results. To address these challenges and simplify nonparametric factor models while maintaining flexibility, we propose the NIFTY framework, which parsimoniously transforms uniform latent variables using 1d non-linear mappings, and then applies a linear generative model. The induced multivariate distribution falls in a flexible class while maintaining simple computation and interpretation. We show identifiability of NIFTY, and empirically study NIFTY with both simulated and real data, observing good performance in dimension reduction in various tasks, including moment estimation and multivariate density estimation.
