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const Q=[
 {q:'單純貝氏分類器被稱為「單純（Naive）」，其最關鍵的大膽假設是什麼？',
  o:['假設所有特徵在現實物理世界中永遠互不相關、完全獨立分佈',
     '假設在「給定類別標籤」的前提下，各特徵之間互相條件獨立，因此能拆解成連乘式',
     '假設所有類別的共變異數矩陣必定是對角矩陣且彼此完全相同',
     '假設特徵的數量永遠只能是二元變數（0 或 1）'], a:1,
  ok:'單純貝氏的「單純」不是指功能簡單，而是指它在已知類別標籤後，大膽假定所有特徵彼此條件獨立，從而把聯合機率拆解成乾淨的連乘式。',
  no:'再想一想：關鍵字是「給定類別之後」的條件獨立，不是「現實中永遠獨立」。'},
 {q:'面對十維二元特徵（l=10）的兩類分類任務，完整聯合模型與單純貝氏模型各需要多少個自由機率參數？',
  o:['完整模型 10 個，單純貝氏 2 個',
     '完整模型 100 個，單純貝氏 20 個',
     '完整模型需要 2¹⁰−1 = 1,023 個，單純貝氏僅需 2l = 20 個，相差超過 51 倍',
     '兩者參數完全相同，皆為 1,024 個'], a:2,
  ok:'完整模型要為 2¹⁰=1,024 種組合估計自由機率（扣除總和為 1 的限制，剩 1,023 個）；單純貝氏只需記錄兩類在 10 個欄位上的機率，共 2×10=20 個，省下 51 倍參數！',
  no:'關鍵公式：完整模型 2ˡ−1，單純貝氏 2l。l=10 時分別是 1,023 與 20。'},
 {q:'對單純貝氏的條件機率乘積比值取自然對數後，為什麼能得到線性判別式 g(x)=wᵀx+w₀？',
  o:['因為取對數會強迫資料分佈自動變成一維標準常態高斯分佈',
     '因為對數運算把各特徵的獨立條件機率連乘積轉化為連加之和，使每個特徵能以常數權重 wᵢ 線性累加其判別貢獻',
     '因為對數會消去特徵空間的所有維度，使所有樣本塌縮到一條直線上',
     '這是數學巧合，只有當 x=(1,0,1) 時才會成立'], a:1,
  ok:'自然對數是嚴格單調遞增函式，取對數不改變排序；更重要的是它把連乘 ∏ 轉成連加 Σ，每個特徵的對數比值就成了線性權重 wᵢ，整體收斂成線性超平面。',
  no:'關鍵在 ln(ab)=ln a+ln b：對數把乘法變加法，而不是改變資料分佈或維度。'},
];
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