Fig. 3.

PRRR identifies optimal rank and is robust to data dimension. a Using synthetic data generated under the PRRR model with a true rank of $R^{\star }=3$, we fit PRRR with a range of rank specifications on the x-axis, where $R^{\star }=3$. The y-axis shows the ELBO values for each model rank. Vertical ticks represent $95\%$ confidence intervals. b Goodness-of-fit $R^2$ values for predictions from PRRR, a full-rank version of PRRR, and a multi-output LASSO model [51] for outcome data with dimension $Q\in \{10,50,100\}$. c Goodness-of-fit $R^2$ values for predictions from PRRR, nn-PRRR, and competing models for outcome data generated from Splatter [60]