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07-log-linear-discriminant.html

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/* ===== Page script ===== */

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let X=[1,0,1];
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  title('取對數的魔法：乘法變加法的線性判別式','The Log Trick: Turning a Product Ratio into a Linear Discriminant',7);

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  showF(['g','wi']);
  wrap('機率連乘容易數值下溢（underflow），也看不出每個特徵各自貢獻多少。取自然對數 ln 是嚴格單調遞增函式，不改變大小順序，卻能把連乘拆成累加，變出一個線性判別式！',90,400,1420,24,16,P.ink,600);

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  wrap('對照第 6 頁：同樣的 x 代入連乘比值 S₁/S₂ 取對數，會得到完全相同的 g(x)。',90,748,730,24,15.5,P.muted,600);

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  txt(`g(x) = ${gx.toFixed(3)}`,878,756,28,gcol,'left',900);
  txt(gx>=0?'g(x) ≥ 0 → 判為 ω₁':'g(x) < 0 → 判為 ω₂',878,792,19,gcol,'left',750);
}
render();

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