I think one objective can be to aim for two main figures for the synthetic experiments:
scatter plot (or density plot) for JRR (x-axis) versus OLS, PLS, CCA, RRR (?) across all hyperparameters (snr, dim_X, etc) for AUC (criterion free identification), sonquist score (criterion-based identification) and prediction error.
Marginal plots : i.e. y-axis=AUC, x-axis=snr, line color = model
PS: sklearn PCA has a 'mle' parameter, which can be used instead of gridsearch the optimal number of componentes.
I think one objective can be to aim for two main figures for the synthetic experiments:
scatter plot (or density plot) for JRR (x-axis) versus OLS, PLS, CCA, RRR (?) across all hyperparameters (snr, dim_X, etc) for AUC (criterion free identification), sonquist score (criterion-based identification) and prediction error.
Marginal plots : i.e. y-axis=AUC, x-axis=snr, line color = model
PS: sklearn PCA has a 'mle' parameter, which can be used instead of gridsearch the optimal number of componentes.