Fig. 2
A A global root-mean-squared-error from the predictions made for all 8 patients, for several machine learning techniques including the median guess model. Models utilized median GBR-NMF scores from biopsies, and prediction RMSEs are provided for the following cell densities: (i) CD68\(^+\), (ii) CD8\(^+\), (iii) CD3\(^+\), (iv) CD68\(^+\) + CD3\(^+\), and the ratio (v) CD68\(^+\)/ CD8\(^+\). B Predictions of CD68\(^+\) + CD3\(^+\) for each patient produced by gradient-boosted trees regression using the average GBR-NMF scores, plotted with an average ± standard deviation alongside the features with the highest importance. C Predictions of CD68\(^+\)/ CD8\(^+\) for each patient produced by elastic net regression using the median GBR-NMF scores, plotted with an average ± standard deviation alongside the features with the highest absolute coefficients. For each patient’s immune cell density predictions, models were optimized based on the training set with that patient’s data left out. The elastic net technique was optimized by grid search of \(\alpha\) and L1 ratio resulting in lowest RMSE, and random forest, gradient-boosted trees and extra trees methods were optimized by iteratively removing features based on importance ranking until the feature list resulted in the lowest RMSE for a patient’s predictions. Top features shown here were ranked by (i) feature importance when utilized in the extra trees model and (ii) highest absolute coefficient value when utilized in the elastic net model. RMSE = root mean squared error; SD = standard deviation.
