Stacking and Ensembling methods in Data Science I understand that using stacking and ensembling has become popular, and these methods can give better results than using a single algorithm.
My question is: What are the reasons, statistical or otherwise, behind the improvement in results?
I also understand that at a high level that combining these methods will combine the predictions from different algorithms. Each algorithm has its own strengths and weaknesses, but not sure how combining them will actually improve the results.
Here is a simple balanced example (50% of the labels are actually T and 50% are actually F), where I think stacking or ensembling algorithms will still give the same result as the original model. In this case, for the ties (1 F and 1 T), I decided to select T. The same problem would occur if I selected F instead. This is a little more complicated if I used the predict_proba, but think the same problem would occur.
It sometimes is called &quot;ensemble learning&quot; where several &quot;weak learners&quot; make a prediction. These predictions are &quot;combined&quot; by some meta-model. A simplistic approach would be that you just use the majority vote. You can also use logistic regression. You can (and should!) of course check the performance of the stacked model(s) by predicting on test data. Related ensemble techniques are boosting and bagging.
Simplified Example: Assume you want to predict a binary outcome. Say you have two different models, which do not perform extremely well, but perform better than random guessing. Also, assume the models are independent. Suppose each of your models makes a correct prediction with $0.8\%$ probability. Now when you have two models, the possible outcomes are:
Correct, Correct:   $0.8*0.8=0.64$
Wrong, Wrong: $0.2*0.2=0.04$
Correct, Wrong: $0.8*0.2=0.16$
Wrong, Correct: $0.2*0.8=0.16$
You see that the probability that both models are wrong is &quot;only&quot; $0.04$. So if you manage to identify the remaining cases as &quot;correct predictions&quot; by some intermediate/meta (stacking) model, you end up with quite a good result. Essentially you would &quot;boost&quot; the expected accuracy of the model(s) from $0.8$ (single model) to $0.64+0.16+0.16=0.96$ (ensemble) here.