HMM学习笔记

原文：http://www.comp.leeds.ac.uk/roger/HiddenMarkovModels/html_dev/main.html

Wangben at mcrc, hit, Harbin 2007.12.17

1.    Introduction

Often we are interested in finding patterns which appear over a space of time. These patterns occur in many areas; the pattern of commands someone uses in instructing a computer, sequences of words in sentences, the sequence of phonemes in spoken words - any area where a sequence of events occurs could produce useful patterns.

我们常常对于找到那些会持续一段时间的模式（pattern）较为感兴趣。这些模式发生在很多的地方；某人在操作电脑时使用命令的模式，句子中词语的序列，说出的词语中的音素（phoneme）的序列—— 只要存在一个序列的事件能够产生有用的模式的任何领域。

Consider the simple example of someone trying to deduce the weather from a piece of seaweed - folklore tells us that 'soggy' seaweed means wet weather, while 'dry' seaweed means sun. If it is in an intermediate state ('damp'), then we cannot be sure. However, the state of the weather is not restricted to the state of the seaweed, so we may say on the basis of an examination that the weather is probably raining or sunny. A second useful clue would be the state of the weather on the preceding day (or, at least, its probable state) - by combining knowledge about what happened yesterday with the observed seaweed state, we might come to a better forecast for today.

考虑一个简单的例子，有人想要从一片海藻中推断出天气——传闻潮湿的海藻表示有雨，而干燥的海藻表示天晴。如果介于中间状态（微湿），则我们无法判断。然而，天气的情况并不是被海藻的状态所约束，所以我们只能说基于观察天气可能是雨或是晴。第二个有用的线索是可以是以前一些天的天气状态（或至少是前些天的可能状态）——通过结合昨天观察海藻状态所得到的知识，我们可以在今天做出更好的预测。

This is typical of the type of system we will consider in this tutorial.

我们将在本文中考虑以下这个典型的系统。

1. First we will introduce systems which generate probabilistic patterns in time, such as the weather fluctuating between sunny and rainy.
   首先我们将介绍一些产生关于时间概率模式的系统，比如波动在晴天和雨天的天气。
2. We then look at systems where what we wish to predict is not what we observe - the underlying system is hidden. In the above example, the observed sequence would be the seaweed and the hidden system would be the actual weather.
   接下来我们将看到一些系统，在这些系统中我们想要预测的东西却是我们所不能观察到的——潜在（underlying）的系统是被隐藏的(hidden)。在上述的例子中，观察序列是海藻而隐藏的系统是实际的天气。
3. We then look at some problems that can be solved once the system has been modeled. For the above example, we may want to know
   然后我们会看到一些问题，一旦系统被建模这些问题都将被解决。在上述的例子中，我们可能想知道：

1. What the weather was for a week given each day's seaweed observation.
   给出了每一天的海藻观测情况，过去一周的天气是怎么样的？
2. Given a sequence of seaweed observations, is it winter or summer? Intuitively, if the seaweed has been dry for a while it may be summer, if it has been soggy for a while it might be winter.
   给出了海藻观测的序列，是冬天还是夏天？直观的来看，如果海藻已经干枯了一段时间，可能现在是夏天，如果海藻已经潮湿了一段时间可能现在是冬天。