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03-product-likelihood-formula.html

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<script>
/* ===== Page script ===== */

/* toy illustrative example: 4 features, class omega_i */
const FEATS=[
  {name:'x₁ 帶書', en:'carries a book', p:0.90},
  {name:'x₂ 戴眼鏡', en:'wears glasses', p:0.40},
  {name:'x₃ 上課時間', en:'class hour', p:0.70},
  {name:'x₄ 背包很重', en:'heavy backpack', p:0.55},
];
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function render(){
  reset();
  title('特徵條件機率連乘：化聯合機率為乘積','The Product Likelihood: One Joint Probability Becomes a Chain of Multiplications',3);

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  showF(['core']);

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  txt('∏ 連乘符號代表什麼？',772,206,19,P.amber,'left',800);
  wrap('把 l 個「一維特徵條件機率」依序乘在一起，取代難以估計的高維聯合機率。',772,234,730,24,16,P.ink,600);
  wrap('The product sign chains l one-dimensional probabilities instead of one intractable joint distribution.',772,290,730,20,13.5,P.muted,550);

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  txt('先鎖定一個類別：ωᵢ（例如「會去圖書館」）　Fix one class first',90,432,19,P.ink,'left',800);

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    txt(`p(${f.name.slice(0,2)}｜ωᵢ) = ${f.p.toFixed(2)}`,840,y+29,19,active?P.ink:P.muted,'right',750);
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  const terms=FEATS.slice(0,step).map(f=>f.p.toFixed(2));
  const expr = terms.length? terms.join('  ×  ') : '（尚未選取特徵 no feature yet）';
  wrap(expr,panelX+30,panelY+64,panelW-60,28,19,P.amber,700);
  const val = terms.length ? FEATS.slice(0,step).reduce((a,f)=>a*f.p,1) : null;
  txt(val===null?'= ?' : `= ${val.toFixed(4)}`,panelX+30,panelY+150,34,val===null?P.muted:P.lime,'left',900);
  wrap(step===FEATS.length
    ? '完成！這就是 p(x|ωᵢ)：四個獨立支援度的連乘總分。'
    : `已納入 ${step} / ${FEATS.length} 個特徵，繼續點擊左側列表累積乘積。`,
    panelX+30,panelY+200,panelW-60,24,15.5,P.muted,600);

  showF(['core']);
}
render();

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