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Add missing corollary and sections reorder
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@ -79,7 +79,10 @@
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\end{description}
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\end{description}
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\end{description}
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\end{description}
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\begin{example}[Axes-aligned rectangles in $\mathbb{R}^2_{[0, 1]}$]
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\section{Axes-aligned rectangles over $\mathbb{R}^2_{[0, 1]}$}
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Consider the instance space $X = \mathbb{R}^2_{[0, 1]}$
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Consider the instance space $X = \mathbb{R}^2_{[0, 1]}$
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and the concept class $\mathcal{C}$ of concepts represented by all the points contained within a rectangle parallel to the axes of arbitrary size.
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and the concept class $\mathcal{C}$ of concepts represented by all the points contained within a rectangle parallel to the axes of arbitrary size.
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@ -108,7 +111,7 @@
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\end{remark}
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\end{remark}
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\begin{theorem}[Axes-aligned rectangles in $\mathbb{R}^2_{[0, 1]}$ PAC learnability]
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\begin{theorem}[Axes-aligned rectangles over $\mathbb{R}^2_{[0, 1]}$ PAC learnability]
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It holds that:
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It holds that:
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\begin{itemize}
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\begin{itemize}
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\item For every distribution $\mathcal{D}$,
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\item For every distribution $\mathcal{D}$,
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@ -156,4 +159,8 @@
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\textit{To be continued\dots}
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\textit{To be continued\dots}
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\end{proof}
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\end{proof}
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\end{theorem}
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\end{theorem}
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\end{example}
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\begin{corollary}
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The concept class of axis-aligned rectangles over $\mathbb{R}^2_{[0, 1]}$ is efficiently PAC learnable.
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\end{corollary}
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