HMM學習(3)-Patterns generated by a hidden process

2007-12-18 20:31 903人閱讀 matrixsystemreturningeachalgorithmsun

3. ?Patterns generated by a hidden process

3.2 When a Markov process may not be powerful enough

In some cases the patterns that we wish to find are not described sufficiently by a Markov process. Returning to the weather example, a hermit may perhaps not have access to direct weather observations, but does have a piece of seaweed. Folklore tells us that the state of the seaweed is probabilistically related to the state of the weather - the weather and seaweed states are closely linked. In this case we have two sets of states, the observable states (the state of the seaweed) and the hidden states (the state of the weather). We wish to devise an algorithm for the hermit to forecast weather from the seaweed and the Markov assumption without actually ever seeing the weather.

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在一些場合我們所希望找到的模式不能夠被馬爾科夫過程很好的描述。回到天氣的例子，一個隱士可能沒有辦法直接觀察到天氣，但是他有一片海藻。傳說海藻與天氣的狀態有一定的聯系。在這個例子中，我們有兩個狀態集合，可觀察的狀態（海藻的狀態）和隱狀態（天氣的狀態）。我們希望為隱士設計一個算法，在不能實際看到天氣的情況下，來從海藻和馬爾科夫假設中預測出天氣的狀態。

A more realistic problem is that of recognizing speech; the sound that we hear is the product of the vocal chords, size of throat, position of tongue and several other things. Each of these factors interacts to produce the sound of a word, and the sounds that a speech recognition system detects are the changing sound generated from the internal physical changes in the person speaking.

一個更實際的問題是語音識別；我們所聽到的聲音是產生自聲帶，喉嚨的大小，舌頭的位置和其他一些東西。每一個因素相互作用產生了詞語的聲音，一個語音識別系統所探測到的聲音都是人說話時內部身體變化所產生的變化的聲音。

Some speech recognition devices work by considering the internal speech production to be a sequence of hidden states, and the resulting sound to be a sequence of observable states generated by the speech process that at best approximates the true (hidden) states. In both examples it is important to note that the number of states in the hidden process and the number of observable states may be different. In a three state weather system (sunny, cloudy, rainy) it may be possible to observe four grades of seaweed dampness (dry, dryish, damp, soggy); pure speech may be described by (say) 80 phonemes, while a physical speech system may generate a number of distinguishable sounds that is either more or less than 80.

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一些語音識別設備認為內部的語音的產物（internal speech production，語言？）是一個隱狀態的序列，發出的聲音是一個可觀察狀態的序列，這個序列由很好的近似了真實狀態（隱狀態）的語音過程所產生。在兩個例子中，非常重要的一點是，隱過程中的狀態的數量與可觀察狀態的數量會很不一樣。在3狀態的天氣系統中（天晴，多云，下雨），可能會觀察到海藻濕潤度的四個等級（干燥，稍干，微濕，潮濕）；純語音可以被80個音素所描述，而一個人體的語音系統可能會產生非常多的不同的聲音，比80多或少。

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In such cases the observed sequence of states is probabilistically related to the hidden process. We model such processes using a hidden Markov model where there is an underlying hidden Markov process changing over time, and a set of observable states which are related somehow to the hidden states.

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在這些情況下，狀態的可觀察序列在一定的概率下與隱過程相關聯。我們使用隱馬爾科夫模型來對這樣的過程進行建模，這里有一個潛在的隱馬爾科夫過程隨時間而改變，以及一個在一定程度上與隱狀態關聯的可觀察的狀態集合。

3.2 Hidden Markov Models

The diagram below shows the hidden and observable states in the weather example. It is assumed that the hidden states (the true weather) are modeled by a simple first order Markov process, and so they are all connected to each other.

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下圖展示了在天氣的例子中的隱狀態以及可觀察狀態。它假定了隱狀態（真實的天氣）通過一個簡單的一階馬爾科夫過程來進行建模，所以他們兩兩之間都有連接。

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The connections between the hidden states and the observable states represent the probability of generating a particular observed state given that the Markov process is in a particular hidden state. It should thus be clear that all probabilities `entering' an observable state will sum to 1, since in the above case it would be the sum of Pr(Obs|Sun), Pr(Obs|Cloud) and Pr(Obs|Rain).

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在隱狀態和可觀察狀態之間的連接表示了在給定馬爾科夫過程停留在一個特定的隱狀態時產生特定的觀察狀態的概率。不難看出，所有的進入一個可觀察狀態的概率之和應該為1，在上面的例子中就應該是Pr(Obs|Sun), Pr(Obs|Cloud) 和 Pr(Obs|Rain)三者的和。？？和底下的矩陣有什么區別？？

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In addition to the probabilities defining the Markov process, we therefore have another matrix, termed the confusion matrix, which contains the probabilities of the observable states given a particular hidden state. For the weather example the confusion matrix might be;

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除了定義了馬爾科夫過程的概率，我們還有另外一個矩陣，稱作混合矩陣（confusion matrix，先驗概率？），它包括了給定特定隱狀態的情況下可觀察狀態的概率。天氣的混合矩陣可以是：

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Notice that the sum of each matrix row is 1.

每行之和為1。

3.3 Summary

We have seen that there are some processes where an observed sequence is probabalistically related to an underlying Markov process. In such cases, the number of observable states may be different to the number of hidden states.

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我們已經看到在一些過程中，可觀察序列是在一定概率下與隱藏的馬爾科夫過程相關聯。在這些例子中，可觀察狀態的數量可以與隱狀態不同。

We model such cases using a hidden Markov model (HMM). This is a model containing two sets of states and three sets of probabilities;

我們使用隱馬爾科夫模型來對這些例子進行建模。這個模型包含了兩個狀態集合和三個概率集（哪三個？轉移概率，confusion matrix，？初始？）。

• hidden states : the (TRUE) states of a system that may be described by a Markov process (e.g., the weather).
• observable states : the states of the process that are `visible' (e.g., seaweed dampness).

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confusion matrix？？？？？？？？？？?

轉載于:https://www.cnblogs.com/hyubz/p/3620375.html

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