### Artificial IntelligenceAIMA Exercises

Consider an ensemble learning algorithm that uses simple majority voting among $K$ learned hypotheses. Suppose that each hypothesis has error $\epsilon$ and that the errors made by each hypothesis are independent of the others’. Calculate a formula for the error of the ensemble algorithm in terms of $K$ and $\epsilon$, and evaluate it for the cases where $K=5$, 10, and 20 and $\epsilon={0.1}$, 0.2, and 0.4. If the independence assumption is removed, is it possible for the ensemble error to be worse than $\epsilon$?

Consider an ensemble learning algorithm that uses simple majority voting among $K$ learned hypotheses. Suppose that each hypothesis has error $\epsilon$ and that the errors made by each hypothesis are independent of the others’. Calculate a formula for the error of the ensemble algorithm in terms of $K$ and $\epsilon$, and evaluate it for the cases where $K=5$, 10, and 20 and $\epsilon={0.1}$, 0.2, and 0.4. If the independence assumption is removed, is it possible for the ensemble error to be worse than $\epsilon$?

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