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09-pitfalls.html
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/* 09 — Four pitfalls, each backed by a number measured on this page set's own runs */
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{q:'EM 需要全新的統計魔法？',qe:'Does EM need some brand-new statistical magic?',t:'沒有魔法，只是「責任度加權」的老朋友！',d:'M 步的均值、變異數、比例，就是 KP09 的樣本統計量，只是每個人的那一票，按「有幾成屬於我」加權。',e:'False. The M-step is the familiar weighted sample mean, variance and proportion.',col:P.cyan},
{q:'責任度可以直接四捨五入成硬分類？',qe:'Why not simply round responsibilities to hard labels?',t:'硬分類丟掉了不確定性。',d:'本例的群分得很開，硬分類也收斂到幾乎相同的結果（log L −86.593 對 −86.590）。但它最大化的是另一個目標，不再保證 log L 單調上升。',e:'On well-separated data both agree, yet hard assignment discards uncertainty and drops the monotonic guarantee.',col:P.lime},
{q:'log L 一路上升 ＝ 找到全域最佳？',qe:'A monotone log L means the global optimum was found?',t:'不保證，起點決定終點！',d:'同一份一維資料，起點 A 收斂到 log L = −155.542，起點 B 收斂到 −153.864。單調上升只保證停在某個山頂。',e:'False. Same data, two initialisations, two different stationary points.',col:P.amber},
{q:'兩個元件的起點可以完全一樣？',qe:'Can both components start at exactly the same place?',t:'對稱死結：永遠分不開。',d:'實測二維資料：兩個中心完全相同時，責任度永遠各 50%，更新後兩元件仍然重合，log L 卡在 −148.41（分開時可達 −86.59）。',e:'False. Identical components receive identical responsibilities and never separate.',col:P.coral}];
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