You are asked to evaluate the performance of two classification models, M1 and M2. The following table shows the probabilities obtained by applying the models to the test set:

Plot the ROC curve for both M1 and M2 on the same graph. Which model do you think is better?

For model M1, suppose you choose the cutoff threshold to be t = 0.5. In other words, any test instances whose posterior probability is greater than t will be classified as a positive example.

(a) Compute the precision, recall, and F-measure for the model at this threshold value.

(b) Repeat the analysis of the above question (question-2) using the same cutoff threshold on model M2.

(c) Compare the F-measure results for both models. Which model is better? Are the results consistent with what you expect from the ROC curve?

Ground M M2 Tuple# truth 1 0.73 0.61 0.69 0.03 0.44 0.68 0.55 0.31 0.67 0.45 0.47 0.09 0.08 0.38 0.15 0.05 0.45 0.01 0.35 0.04 4 6 10 Ground M M2 Tuple# truth 1 0.73 0.61 0.69 0.03 0.44 0.68 0.55 0.31 0.67 0.45 0.47 0.09 0.08 0.38 0.15 0.05 0.45 0.01 0.35 0.04 4 6 10