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09-interactive-lab.html

<!doctype html><html lang="zh-Hant"><head><meta charset="utf-8"><meta name="viewport" content="width=device-width,initial-scale=1"><title>KP16 09 Interactive Lab</title>
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</head><body><div class="wrap"><div class="stage" id="stage"><canvas id="c" width="1600" height="900"></canvas><div id="math-layer"></div><div class="hint">互動：點擊 / 拖曳 • Click / Drag</div></div></div>
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<script>
/* ===== Page script ===== */

let L=6;
let X=[1,0,1];
const P1=[0.8,0.3,0.7], Q1=[0.4,0.6,0.5];
const LOGMAX=Math.log10(Math.pow(2,20)-1);

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function render(){
  reset();
  title('動態探索實驗室：維度 × 條件獨立 × 乘積決策','Interactive Lab: Dimension, Independence, and Product-Score Decisions',9);

  /* ======================= LEFT: dimension & parameter scaling ======================= */
  rr(60,170,760,672,24,P.panel,'#ffffff14',2);
  txt('A　特徵維度與參數規模',90,204,20,P.ink,'left',850);
  txt('Dimension l controls how many parameters each model needs',90,230,14,P.cyan,'left',600);

  [3,6,10,15,20].forEach((v,i)=>btn('l='+v,90+i*132,256,118,38,()=>{L=v;render()},L===v,P.cyan,16));
  slider(130,340,640,1,20,L,v=>{L=Math.round(v);render()},'特徵維度 l (1–20)',v=>'l = '+v.toFixed(0));

  const fullParams=Math.pow(2,L)-1, naiveParams=2*L, ratio=fullParams/naiveParams;
  const barX=90,maxW=700;
  const fullW=Math.max(8,(Math.log10(Math.max(1,fullParams))/LOGMAX)*maxW);
  const naiveW=Math.max(8,(Math.log10(Math.max(1,naiveParams))/LOGMAX)*maxW);

  txt(`完整聯合模型 2ˡ−1 = ${fmtBig(fullParams)}`,barX,410,18,P.coral,'left',800);
  rr(barX,422,maxW,30,8,'#ffffff10'); rr(barX,422,fullW,30,8,P.coral+'dd');
  txt(`單純貝氏 2l = ${naiveParams}`,barX,478,18,P.lime,'left',800);
  rr(barX,490,maxW,30,8,'#ffffff10'); rr(barX,490,naiveW,30,8,P.lime+'dd');

  rr(barX,548,maxW,110,16,'#ffffff08');
  txt(`節省倍率 = ${fullParams>=naiveParams?(ratio>=100?ratio.toFixed(0):ratio.toFixed(2)):ratio.toFixed(2)}×`,barX+20,580,22,P.amber,'left',850);
  wrap(fullParams>=naiveParams
    ? `l = ${L} 時，完整模型要估 ${fmtInt(fullParams)} 個參數，單純貝氏只要 ${naiveParams} 個。`
    : `l = ${L} 太小，優勢還沒顯現；l ≥ 3 後差距才會急遽放大。`,
    barX+20,610,maxW-40,24,16,P.ink,600);

  wrap('拖曳滑桿觀察：維度越高，指數模型越快撐不住，單純貝氏仍穩健線性成長。',90,682,700,25,16,P.muted,600);

  /* ======================= RIGHT: 3-feature product-score decision ======================= */
  rr(840,170,700,672,24,P.panel2,'#ffffff14',2);
  txt('B　三維特徵開關與乘積分數決策',870,204,20,P.ink,'left',850);
  txt('Toggle each bit and watch the product scores race',870,230,14,P.amber,'left',600);

  const swX=[870,1070,1270];
  X.forEach((v,i)=>btn(`x${i+1} = ${v}`,swX[i],256,170,46,()=>{X[i]=1-X[i];render()},true,v===1?P.lime:P.coral,19));

  let s1=1,s2=1;
  for(let j=0;j<3;j++){ s1*= X[j]===1?P1[j]:1-P1[j]; s2*= X[j]===1?Q1[j]:1-Q1[j]; }
  const total=s1+s2, pr1=s1/total, win=s1>=s2?1:2;

  const sbX=870,sbW=620,maxScore=Math.max(s1,s2,0.01);
  txt(`S₁ = ${s1.toFixed(3)}`,sbX,344,19,C1,'left',800);
  rr(sbX,356,sbW,30,8,'#ffffff10'); rr(sbX,356,Math.max(6,(s1/maxScore)*sbW),30,8,C1+'dd');
  txt(`S₂ = ${s2.toFixed(3)}`,sbX,412,19,C2,'left',800);
  rr(sbX,424,sbW,30,8,'#ffffff10'); rr(sbX,424,Math.max(6,(s2/maxScore)*sbW),30,8,C2+'dd');

  rr(870,480,620,96,16,win===1?'#63b3ed1c':'#ff7b721c',win===1?C1:C2,2);
  txt(`判決 ω̂ = ω${win}`,900,512,24,win===1?C1:C2,'left',900);
  txt(`後驗機率 ≈ ${(Math.max(pr1,1-pr1)*100).toFixed(1)}%`,900,548,18,win===1?C1:C2,'left',700);

  /* log-linear cross-check */
  const W=[0,1,2].map(j=>Math.log((P1[j]*(1-Q1[j]))/(Q1[j]*(1-P1[j]))));
  const W0=[0,1,2].reduce((a,j)=>a+Math.log((1-P1[j])/(1-Q1[j])),0);
  const gx = W.reduce((a,w,j)=>a+w*X[j],0)+W0;
  rr(870,600,620,210,18,P.panel,P.amber+'55',2);
  showF(['g']);
  txt(`g(x) = ln(S₁/S₂) = ${Math.log(s1/s2).toFixed(3)}`,900,696,18,P.ink,'left',700);
  txt(`w·x + w₀ = ${gx.toFixed(3)}`,900,726,18,P.ink,'left',700);
  txt(Math.abs(gx-Math.log(s1/s2))<1e-6?'✓ 兩種算法完全一致 Consistent':'',900,758,16,P.lime,'left',650);
  txt(`x = (${X.join(', ')})`,1460,758,18,P.amber,'right',800);
}
render();

</script></body></html>