一、马尔可夫链及其应用

[b] 一、马尔可夫链[/b][br][br] 随机过程描述的是一个量随时间可能的变化。在这个过程里,每一个时刻变化的方向都是不确定的,随机过程就是由这一系列不确定的随机变量组成的。每一个时刻系统的状态都[br]由一个随机变量表述,整个过程则构成一个随机过程的实现。[br][br] 知道了什么是随机过程后,可以试想一个最简单的随机过程,这个过程由 N 步组成,每一步都有两个选择(0,1),那么可能的路径就有 2 的 N 次方个,这个随机过程就要由 [math]2^N[/math] 这个指数级别个数的概率来描述,而这个指数级别太大,在现实中计算难度较大,所以需要使用马尔可夫过程(Markov Processes):随机过程的每一步的结果与且仅与上一步有关,与其他无关。[br][br] 马尔可夫性:在时刻 [math]T_0[/math] 所处状态为已知的条件下,过程在时刻 [math]T>T_o[/math]所处状态的条件分布过程与时刻 [math]T_0[/math] 之前所处的状态无关的特性称为马尔可夫性或无后效性。具有马尔可夫性的随机过程称为马尔可夫过程。[br] [br] 马尔可夫链:时间和状态都是离散的马尔可夫过程。[br][br] 状态空间中经过一个状态到另一个状态的转换随机过程,该过程要求具备无记忆的性质:下一状态的概率分布只能由当前状态决定,在时间序列中它前面的事件均与之无关,如图2-9-3 所示。[br][center][img]https://s21.ax1x.com/2025/02/20/pEQBkTI.png[/img][/center] 图 2-9-3 马尔可夫链示意
马尔可夫链是一个随机系统,它必须满足两个条件:[br][br] ① 系统任意时刻可以用有限个可能状态之一来描述;[br][br] ② 系统无后效性,即某阶段的状态一旦确定,则此后过程的演变不再受此前各种状态及决策的影响。[br][br] 马尔可夫链的数学表达如下。[br][br] 状态向量:[br] [br] [math]X^{\left(n\right)}=\left(x^{\left(n\right)}_1x^{\left(n\right)}_2...x^{\left(n\right)}_k\right)[/math][br] [br] ● 概率向量的每个元素都是概率,并且元素之和为 1;[br][br] ● 系统的可能状态数有[math]k[/math]个;[br][br] ● 向量中各个元素分别表示第 [math]n[/math] 次观测第 [math]i[/math]个状态的概率;[br][br] ● [math]x^0[/math]被称为初始状态。[br][br] 转移概率矩阵:[br] [img]https://s21.ax1x.com/2025/02/20/pEQBKXQ.png[/img][br][br] ● [math]p_{ij}\left(i,j=1,2,...,k\right)[/math] 表示这次观测前状态为[math]i[/math],现在观测是状态为 [math]j[/math]的概率;[br][br] ●[math]P[/math]矩阵元素非负;[br][br] ● 每一行的元素之和都为 1。[br][br] 根据无后效性,可以得出: [math]X^{_{^{(n+1}})}=X^{\left(n\right)}P[/math] 。[br][br] 从而, [math]X^{_{^{(n+1}})}=X^{\left(0\right)}P^n[/math] 。[br][br] 由于某一时刻状态转移的情况只依赖前一个状态,那么只要求出系统中任意两个状态之间的转移概率,这个马尔可夫链的模型就确定了。
[b] 二、马尔可夫链的应用[/b][br][br] (一)随机漫步[br][br] 马尔可夫链的一个典型例子是随机漫步,其每一步的状态是在图形中的点,每一步可以移动到任何一个相邻的点,且移动到每一个点的概率都是相同的,如图 2-9-4所示。随机漫步程序的VBA 语言程序及动态演示可[color=#0000ff][b][url=https://pan.baidu.com/disk/main#/index?category=all&path=%2F%E5%A4%A7%E6%95%B0%E6%8D%AE%E7%AE%97%E6%B3%95%E5%9F%BA%E7%A1%80-%E8%A7%A3%E6%9E%90%E4%B8%8E%E6%8E%A2%E7%B4%A2%2F11.%E9%A9%AC%E5%B0%94%E7%A7%91%E5%A4%AB%E9%93%BE%E5%8F%8A%E8%87%AA%E7%84%B6%E8%AF%AD%E8%A8%80%E5%A4%84%E7%90%86%2F%E9%A9%AC%E5%B0%94%E7%A7%91%E5%A4%AB%E9%93%BE]下载[/url][icon]/images/ggb/toolbar/mode_zoomin.png[/icon][/b][/color]查看。
[center][size=100] 图 2-9-4 随机漫步示意[/size][size=100][/size][/center]
(二)病情预测[br][br] 艾滋病毒感染者病情发展有这样几个阶段(状态):[br][br] ① 无临床症状(HIV asymptomatic);[br][br] ② 有临床病状(HIV symptomatic);[br][br] ③ 获得性免疫缺陷综合征(AIDS);[br][br] ④ 死亡(death)。[br][br] 其转移矩阵如表 2-9-1 所示。[br] 表 2-9-1 艾滋病毒感染者病情转移矩阵[br][img]data:image/png;base64,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[/img]
某地区艾滋病感染者一年后由一个状态转移到另一个状态的概率如表 2-9-1 所示。如果目前该地区感染者处于各状态的比例如表 2-9-2 所示。那么三年后,该地区感染者处于各状态的比例如何?[br] 表 2-9-2 艾滋病毒感染者处于各状态的比例[br][img]data:image/png;base64,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[/img][br][br] 表 2-9-1 就是确定的转移概率矩阵 p ,它是时间齐次性的,也就是转移概率矩阵 p 保持不变,第一年到第二年的转移概率矩阵与第二年到第三年的转移概率矩阵是一样的。[br] 有了这个转移概率矩阵 p ,再加上已知的初期状态分布矩阵 S ,就可以计算该地区第 N年的艾滋病状态分布。[br][br] 第一年该地区的艾滋病状态分布矩阵 [math]s_1=s_0\cdot p[/math] (矩阵相乘),如表 2-9-3 所示。[br][br] 表 2-9-3 第一年艾滋病状态分布比例[br][img]data:image/png;base64,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[/img][br][br] 第二年该地区的艾滋病状态分布矩阵 [math]s_2=s_1\cdot p[/math] (只和 s1 有关),如表 2-9-4 所示[br][br] 表 2-9-4 第二年艾滋病状态分布比例[br][img]data:image/png;base64,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[/img][br][br] 第三年该地区的艾滋病状态分布矩阵[math]s_3=s_2\cdot p[/math] (只和 s2 有关),如表 2-9-5 所示。[br][br] 表 2-9-5 第三年艾滋病状态分布比例[br][img]data:image/png;base64,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[/img][br][br] 如果仅仅计算某个感染者的概率,显然病情发展与该患者获得的治疗有着密切关系,但如果研究某个地区的艾滋病患者,那么在无外界因素干预,如国家加大艾滋病治疗投入或艾滋病特效药研发成功等,马尔可夫链模型是个不错的预测模型。
[br] (三)语音识别及自然语言处理[br][br] 让机器“听懂”人类的语言,需要用到两个马尔可夫模型:[br][br] (1)声学模型:利用 HMM 建模(隐马尔可夫模型)。HMM 是指这一马尔可夫模型的内部状态外界不可见,外界只能看到各个时刻的输出值。对于语音识别系统,输出值通常就是从各个帧计算而得的声学特征。[br][br] (2)语言模型:N-Gram 算法,简单有效,所以应用也最广泛。它基于独立输入假设:第[math]n[/math] 个词的出现只与前面 [math]n-1[/math]个词相关,而与其他任何词都不相关。整句的概率就是各个词出现概率的乘积。这些概率可以通过直接从语料中统计 [math]n[/math] 个词同时出现的次数得到。[br][br] 简单来说,人们利用马尔可夫模型,来计算事件的状态转移概率矩阵,除了语音识别,只要随机过程具有马尔可夫性,都少不了应用马尔可夫链。

Information: 一、马尔可夫链及其应用