Can we generalize all ensemble methods by using voting? Do boosting methods also use voting to get the weak learners into the final model?
My understanding of the technique:
- Boosting: Continuously adds in weak learner to boost the data points that were not correctly classified.
- Ensemble technique: Uses multiple learners to obtain a better prediction than from one alone. This is explained in wikipedia.
Best Answer
Boosting can generally be understood as (weighted) voting
In the case of boosting, one of its inventors gives an affirmative answer in this introduction to AdaBoost (emphasis mine):
So yes, the final model returned is a weighted vote of all the weak learners trained to that iteration. Likewise, you'll find this snippet on Wikipedia about boosting in general:
Also note the mention therein that the original boosting algorithms used a "majority." The notion of voting is pretty firmly baked into boosting: Its guiding principle is to improve an ensemble at each iteration by adding a new voter, then deciding how much weight to give each vote.
This same intuition carries for the example of gradient boosting: At each iteration $m$ we find a new learner $h_m$ fitted to pseudo-residuals, then optimize $\gamma_m$ to decide how much weight to give $h_m$'s "vote."
Extending to all ensemble methods runs into counterexamples
As it is, some would find that even the notion of weighting stretches the voting metaphor. When considering whether to extend this intuition to all ensemble learning methods, consider this snippet:
And this one on the example ensemble method of stacking:
If you're defining ensemble methods to include stacking methods with an arbitrary combiner, you can construct methods that, in my view, stretch the notion of voting beyond its limit. It's difficult to see how a collection of weak learners combined via a decision tree or neural network can be viewed as "voting." (Leaving aside the also difficult question of when that method might prove practically useful.)
Some introductions describe ensembles and voting as synonymous; I'm not familiar enough with recent literature on these methods to say how these terms are generally applied recently, but I hope this answer gives an idea of how far the notion of voting extends.