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05-parameter-savings.html
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/* ===== Page script ===== */
/* ===== Shared helpers for KP18: DAG drawing, parent sets, CPT parameter counting ===== */
const C1='#63b3ed',C2='#ff7b72';
const NM=['x₁','x₂','x₃','x₄','x₅','x₆'];
const POS6=[[.10,.26],[.10,.76],[.38,.93],[.42,.50],[.70,.22],[.90,.60]]; /* normalised node positions */
const EDGES_BN=[[2,3],[1,4],[2,4],[4,5],[4,6],[5,6]]; /* (parent, child), 1-indexed */
const EDGES_FULL=(()=>{const e=[];for(let j=2;j<=6;j++)for(let i=1;i<j;i++)e.push([i,j]);return e})();
const parentsOf=(E,i)=>E.filter(e=>e[1]===i).map(e=>e[0]);
const nParams=(E,n=6)=>{let s=0;for(let i=1;i<=n;i++)s+=Math.pow(2,parentsOf(E,i).length);return s};
function hasCycle(E,n=6){const adj={};for(let i=1;i<=n;i++)adj[i]=[];E.forEach(e=>adj[e[0]].push(e[1]));const st={};
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return out}
const SUPM={'0':'⁰','1':'¹','2':'²','3':'³','4':'⁴','5':'⁵','6':'⁶','7':'⁷','8':'⁸','9':'⁹','-':'⁻'};
const sup=n=>String(n).split('').map(c=>SUPM[c]||c).join('');
/* 05 — Where the savings come from: binary CPT slots, sum over nodes of 2^|A_i| */
let mode=1,sel=4;
const MODES=[['Naive Bayes',[],C1],['貝氏網路',EDGES_BN,P.lime],['完整聯合',EDGES_FULL,C2]];
function render(){
reset();title('數值實戰：參數到底省在哪','Numerical demo: where do the parameters go?',5);
const E=MODES[mode][1],par=parentsOf(E,sel),tot=nParams(E);
rr(60,170,740,680,24,P.panel,'#ffffff14',2);
MODES.forEach((m,i)=>btn(m[0],90+i*230,186,214,44,()=>{mode=i;render()},mode===i,m[2],16));
const pts=drawDAG({x:100,y:262,w:660,h:300},POS6,E,{sel,r:22,thin:E.length>8});
pts.forEach((p,i)=>area(p[0]-26,p[1]-26,52,52,()=>{sel=i+1;render()}));
txt(`節點 x${'₀₁₂₃₄₅₆'[sel]} 的條件機率表（父節點 k = ${par.length}）`,90,596,18,P.amber,'left',850);
const rows=Math.pow(2,par.length),show=Math.min(rows,8);
for(let r=0;r<show;r++){const y=632+r*25;rr(90,y-11,680,23,6,r%2?'#ffffff08':'#ffffff0f');
const cond=par.length?par.map((p,j)=>`${NM[p-1]}=${(r>>(par.length-1-j))&1}`).join(', '):'無條件（根節點）';
txt(par.length?`P(x${'₀₁₂₃₄₅₆'[sel]}=1 | ${cond})`:`P(x${'₀₁₂₃₄₅₆'[sel]}=1)`,106,y,15,P.ink,'left',650);txt('θ',740,y,15,P.amber,'right',800)}
txt(rows>show?`… 共 ${rows} 列，每列 1 個自由參數`:`共 ${rows} 列，每列 1 個自由參數`,90,836,14,P.muted,'left',600);
rr(830,170,710,680,24,P.panel,'#ffffff14',2);
txt('逐節點相加：Σ 2^|Aᵢ|',860,205,21,P.ink,'left',850);
let s=[];for(let i=1;i<=6;i++){const k=parentsOf(E,i).length;s.push(Math.pow(2,k));
const y=250+(i-1)*34,on=i===sel;txt(`x${'₀₁₂₃₄₅₆'[i]}`,870,y,17,on?P.amber:P.ink,'left',850);txt(`|A| = ${k}`,930,y,15,P.muted,'left',650);
rr(1040,y-9,Math.max(6,300*s[i-1]/32),18,6,(on?P.amber:MODES[mode][2])+'cc');txt(`2^${k} = ${s[i-1]}`,1040+Math.max(6,300*s[i-1]/32)+10,y,15,P.ink,'left',750)}
txt(`總計 = ${s.join(' + ')} = ${tot}`,860,462,24,MODES[mode][2],'left',900);
[['NB',6,C1],['BN',nParams(EDGES_BN),P.lime],['Full',63,C2]].forEach((b,i)=>{const y=512+i*34;txt(b[0],870,y,15,P.muted,'left',700);rr(920,y-9,420*b[1]/63,18,6,b[2]+'cc');txt(String(b[1]),920+420*b[1]/63+10,y,15,P.ink,'left',800)});
rr(860,622,650,208,18,'#f6c85f14',P.amber,2);
txt('口徑釋疑：13 還是 14？',884,652,19,P.amber,'left',900);
wrap('原講義標示 13；但依指定的父集合逐節點相加（二元 CPT，每節點 2^|A| 個自由參數）是 1+1+2+4+2+4 = 14。本專案採 14，並由本頁即時加總驗證。不論 13 或 14，相較完整分佈的 63 都少了約八成（14 對 63：省 77.8%）。',884,676,606,26,16,P.ink,600);
showF([]);
}
render();
</script></body></html>