From 6af7c3775ec18878441684310d30c78990aa6231 Mon Sep 17 00:00:00 2001 From: qiwang067 Date: Sun, 7 Feb 2021 09:59:42 +0800 Subject: [PATCH] fix ch2 typos --- docs/chapter2/chapter2.md | 21 ++++++++++++++------- docs/chapter2/img/2.5.png | Bin 206830 -> 85604 bytes 2 files changed, 14 insertions(+), 7 deletions(-) diff --git a/docs/chapter2/chapter2.md b/docs/chapter2/chapter2.md index 53b9d26..5f4fa01 100644 --- a/docs/chapter2/chapter2.md +++ b/docs/chapter2/chapter2.md @@ -18,7 +18,7 @@ ### Markov Property -![](img/2.4.png)如果一个状态转移是符合马尔可夫的,那就是说一个状态的下一个状态只取决于它当前状态,而跟它当前状态之前的状态都没有关系。 +如果一个状态转移是符合马尔可夫的,那就是说一个状态的下一个状态只取决于它当前状态,而跟它当前状态之前的状态都没有关系。 我们设状态的历史为 $h_{t}=\left\{s_{1}, s_{2}, s_{3}, \ldots, s_{t}\right\}$($h_t$ 包含了之前的所有状态),如果一个状态转移是符合马尔可夫的,也就是满足如下条件: $$ @@ -31,9 +31,9 @@ $$ 从当前 $s_t$ 转移到 $s_{t+1}$ 这个状态,它是直接就等于它之前所有的状态转移到 $s_{t+1}$。如果某一个过程满足`马尔可夫性质(Markov Property)`,就是说未来的转移跟过去是独立的,它只取决于现在。**马尔可夫性质是所有马尔可夫过程的基础。** -### Markov Process +### Markov Process/Markov Chain -![](img/2.5.png) +![](img/2.5.png ':size=500') 首先看一看`马尔可夫链(Markov Chain)`。举个例子,这个图里面有四个状态,这四个状态从 $s_1,s_2,s_3,s_4$ 之间互相转移。比如说从 $s_1$ 开始, @@ -47,7 +47,16 @@ $$ * 有 0.2 的概率转移到 $s_3$ , * 有 0.5 的概率留在这里。 -我们可以用`状态转移矩阵(State Transition Matrix)`来描述这样的状态转移。状态转移矩阵类似于一个 conditional probability,当我们知道当前我们在 $s_t$ 这个状态过后,到达下面所有状态的一个概念。所以它每一行其实描述了是从一个节点到达所有其它节点的概率。 +我们可以用`状态转移矩阵(State Transition Matrix)` $P$ 来描述状态转移 $p\left(s_{t+1}=s^{\prime} \mid s_{t}=s\right)$,如下式所示。 +$$ +P=\left[\begin{array}{cccc} +P\left(s_{1} \mid s_{1}\right) & P\left(s_{2} \mid s_{1}\right) & \ldots & P\left(s_{N} \mid s_{1}\right) \\ +P\left(s_{1} \mid s_{2}\right) & P\left(s_{2} \mid s_{2}\right) & \ldots & P\left(s_{N} \mid s_{2}\right) \\ +\vdots & \vdots & \ddots & \vdots \\ +P\left(s_{1} \mid s_{N}\right) & P\left(s_{2} \mid s_{N}\right) & \ldots & P\left(s_{N} \mid s_{N}\right) +\end{array}\right] +$$ +状态转移矩阵类似于一个 conditional probability,当我们知道当前我们在 $s_t$ 这个状态过后,到达下面所有状态的一个概念。所以它每一行其实描述了是从一个节点到达所有其它节点的概率。 ### Example 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