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11-summary.html

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/* 11 — Summary: four master take-aways, each with its core formula */
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 {zh:'EM 在處理什麼問題？',en:'What problem does EM solve?',col:P.cyan,
  items:[['混合密度','p(x)=\\sum_{j=1}^{J}p(x\\mid j)\\,P_j'],['不完整資料的對數概似','\\ln L=\\sum_{k}\\ln\\sum_{j}P_j\\,p(x_k\\mid j)']],
  text:'資料來自好幾個元件，但每筆資料的來源標籤遺失。對數裡面包加總，讓參數無法直接分離求解。'},
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  items:[['軟性責任度','r_{kj}=\\dfrac{p(x_k\\mid j;\\Theta^{(t)})\\,P_j^{(t)}}{\\sum_{m}p(x_k\\mid m;\\Theta^{(t)})\\,P_m^{(t)}}']],
  text:'用目前的參數，為每筆資料算出屬於各元件的百分比猜測，而不是一刀切的硬分類。'},
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  text:'以責任度為權重，重新計算加權平均、加權變異數與加權比例。'},
 {zh:'為什麼可以放心迭代？',en:'Why is iterating safe?',col:P.amber,
  items:[['單調不減','\\log L(\\Theta^{(t+1)})\\ge\\log L(\\Theta^{(t)})']],
  text:'保證每一輪只升不降，會收斂到穩定點；但可能是區域性山頂，所以起點要拉開、要多試幾次。'}];
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