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Consider an ensemble classifier constructed by T rounds of AdaBoost on N training examples. \begin{align} H(\mathbf{x}) = \sum_{t= 1}^{T} \alpha_{t} h_{t}(\mathbf{x}) \end{align}

The next classifier: $h_{T+1}$ is added to the ensemble, by minimizing the training error weighted by $W_{1}^{T}$ ... $W_{N}^{T}$. For the question, I am trying to figure out how to show that $$\epsilon_{T + 1}$$ (the training error of $h_{T+1}$) weighted by the updated weights $W_{1}^{T+1}$ ... $W_{N}^{T+1}$ equals $\frac{1}{2}$.

rerecodes
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  • Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. – Community Apr 01 '23 at 06:10
  • What is Adaboost ? – Jean Marie Apr 01 '23 at 06:47
  • Please add details on the definition of $h_t$ and the weight updates – Claudio Moneo Apr 01 '23 at 13:03
  • @ClaudioMoneo $h_{t}$ is just a single weak classifier chosen for a specific t, which is a round of the adaboost. $H_(x)$ is the combination of all the weak classifiers used for the total rounds (T) that Adaboost is implemented: $H_\mathbf(x) = \alpha_{1} h_{1}\mathbf(x) + ... + \alpha_{T} h_{T}\mathbf(x)$ – rerecodes Apr 01 '23 at 17:25
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    @JeanMarie Adaboost is a type of boosting algorithm. – rerecodes Apr 01 '23 at 19:22

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