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隱馬爾科夫模型HMM自學(xué) （5-2）Viterbi Algorithm

書(shū)接前文，viterbi算法已經(jīng)基本成形......

崔曉源 翻譯

一般化上一篇最后得到的公式我們可以把概率的求解寫(xiě)成：

2d. 反向指針,

考慮下面trellis

現在我們可以得到到達每一個(gè)中間或者終點(diǎn)狀態(tài)的概率最大的路徑。但是我們需要采取一些方法來(lái)記錄這條路徑。這就需要在每個(gè)狀態(tài)記錄得到該狀態(tài)最優(yōu)路徑的前一狀態(tài)。記為：

這樣argmax操作符就會(huì )選擇使得括號中式子最大的索引j。

如果有人問(wèn)，為什么沒(méi)有乘以混淆矩陣中的觀(guān)察概率因子。這是因為我們關(guān)心的是在到達當前狀態(tài)的最優(yōu)路徑中，前一狀態(tài)的信息，而與他對應的觀(guān)察狀態(tài)無(wú)關(guān)。

2e. viterbi算法的兩個(gè)優(yōu)點(diǎn)

1）與Forward算法一樣，它極大的降低了計算復雜度

2）viterbi會(huì )根據輸入的觀(guān)察序列，“自左向右”的根據上下文給出最優(yōu)的理解。由于viterbi會(huì )在給出最終選擇前考慮所有的觀(guān)察序列因素，這樣就避免了由于突然的噪聲使得決策原理正確答案。這種情況在真實(shí)的數據中經(jīng)常出現。

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下面給出viterbi算法完整的定義1. Formal definition of algorithm

The algorithm may be summarised formally as:

For each i,, i = 1, ... , n, let :

- this intialises the probability calculations by taking the product of the intitial hidden state probabilities with the associated observation probabilities.

For t = 2, ..., T, and i = 1, ... , n let :

- thus determining the most probable route to the next state, and remembering how to get there. This is done by considering all products of transition probabilities with the maximal probabilities already derived for the preceding step. The largest such is remembered, together with what provoked it.

Let :

- thus determining which state at system completion (t=T) is the most probable.

For t = T - 1, ..., 1

Let :

- thus backtracking through the trellis, following the most probable route. On completion, the sequence i1 ... iT will hold the most probable sequence of hidden states for the observation sequence in hand.

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