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Suppose I have two binary classifiers, A and B. Both are trained on the same set of data, and produce predictions on a different (but same for both classifiers) set of data. The precision for A is high and the recall is low, whereas the precision for B is low and the recall is high. Is there a way to combine these two models where I can get the precision from one and recall from the other, or possibly use the metrics from one to improve those of the other?

For example, let's say these are the metrics:

A

Precision: 0.91

Recall: 0.35

B

Precision: 0.44

Recall: 0.90

As these are binary classifiers, my labels are 1 and 0, and my class of interesting is 1 (so the metrics above are for predicting 1s).

Let's say model A predicts 10 1s, and model B predicts 70 1s.

It is safe for me to say that of the 10 1s that model A has predicted, 9 are true positives.

It is also safe for me to say that of the 70 1s that model B has predicted, 60% are false positives, but the rest are 90% of the true positives in the dataset.

My question is, is there some method for me to combine these results so that I can obtain all 50 true positives from the dataset?

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What you are actually looking for is Micro and Macro Precision and Recall.

If you directly have the precision and the recall values calculated, then all that's possible is only Macro Precision and Macro Recall.

Macro Formula goes as follows:

Macro_Precision = (Precision1 + Precision2) / 2

Macro_Recall = (Precision1 + Precision2) / 2

But if you have more granular details such as True Positives and False Positives, then you can compute even compute the Micro Precision and Micro Recall. Their formula goes as follows:

Micro_Precision = (TP1 + TP2) / (TP1 + TP2 + FP1 +FP2)

Micro_Recall = (TP1 + TP2) / (TP1 + TP2 + FN1 + FN2)

Micro and Macro have their own significance, you use Micro when you want insight in granular level, and this helps in cases where the Dataset is imbalanced.

Vote up, if you find this helpful ;)

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  • $\begingroup$ Sorry I don't think this helps me. I would like to know if I can use the given metrics to maximize the amount of TPs out of the dataset $\endgroup$ – user8115948 Mar 27 at 14:11
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You want to ensemble your two algorithms. The way to do that is to not just use e.g. sklearn's precision and recall metric functions, but to actually obtain probabilities for being positive (most models can output this with a simple function call), and take the average of those probabilities between your two (or more) binary classifiers. Then, test a range of probability thresholds beyond which you might label something positive, and evaluate the impact on recall and precision. This is a pretty common approach to obtaining better results through utilizing the strengths of different prediction algorithms.

Just some pythonic pseudo-code to demonstrate:

recall = []
precision = []
for threshold in [0.1, 0.2, 0.3, ..., 0.9]:
    df_of_mean_probabilities['label'] = df_of_mean_probabilities > threshold
    recall.append(TP/(TP + FN))
    precision.append(TP/(TP + FP))
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