Fig. 4.

PRRR is robust to rank misspecification. Using synthetic data generated from the PRRR model with a true rank of $R^{\star }=3$, we fit PRRR with a range of rank specifications (x-axis). We made predictions for a held-out dataset and computed the $R^2$ coefficient of determination, repeating this ten times for each rank. The y-axis shows the $R^2$ value between the predicted values and the true values on held-out samples. Boxes show the median and upper and lower quartiles, and whiskers extend to 1.5 times the interquartile range. a Maximum a posteriori estimates (MAP); b Variational inference (VI); c Comparison with Gaussian RRR [48] and LASSO [51]