VIPurPCA: Visualizing and Propagating Uncertainty in Principal Component Analysis

This work offers a generic example for the visualization of uncertainty propagated through nonlinear algorithms by automatic differentiation. Scientists use increasingly elaborate algorithms to assess and analyze empirical data. Uncertainty estimates — error bars — are crucial for scientific analysis, but many modern computational analysis methods do not propagate uncertainty from their inputs to their outputs. Our example treatment of PCA combines the classic notion of linearization for error propagation with the power of modern automatic differentiation, and can be applied to other methods, too. We provide a visualization technique to go alongside this approach: Animations along orbits of the probability distribution provide an additional visual channel to represent uncertainty even in plots that are already visually dense as point estimates.