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Statistical classification is the problem of identifying the sub-population to which new observations belong, where the identity of the sub-population is unknown, on the basis of a training set of data containing observations whose sub-population is known. Therefore these classifications will show a variable behavior which can be studied by statistics.

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weak learning of 3-piece classifiers using decision stumps

For example, let $g = sign(x-\theta)\cdot b$ s.t. $P_{\mathcal D}(\{x:\theta\le x \le\theta_1\})= 0.4$ That is, $\theta = -\infty$. Then, $g$ agrees with $\hat h_{\theta_1, \theta_2, b}(x)$ on $[\ …
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