首先看一下来自Wolfram的定义
马尔可夫链是随机变量{X_t}的集合（t贯穿0,1,...），给定当前的状态，未来与过去条件独立。
Wikipedia的定义更清楚一点儿
...马尔可夫链是具有马尔可夫性质的随机过程...[这意味着]状态改变是概率性的，未来的状态仅仅依赖当前的状态。
马尔可夫链具有多种用途，现在让我看一下如何用它生产看起来像模像样的胡言乱语。
算法如下,
代码如下
import random
class Markov(object):
def __init__(self, open_file):
self.cache = {}
self.open_file = open_file
self.words = self.file_to_words()
self.word_size = len(self.words)
self.database()
def file_to_words(self):
self.open_file.seek(0)
data = self.open_file.read()
words = data.split()
return words
def triples(self):
""" Generates triples from the given data string. So if our string were
"What a lovely day", we'd generate (What, a, lovely) and then
(a, lovely, day).
"""
if len(self.words) < 3:
return
for i in range(len(self.words) - 2):
yield (self.words[i], self.words[i+1], self.words[i+2])
def database(self):
for w1, w2, w3 in self.triples():
key = (w1, w2)
if key in self.cache:
self.cache[key].append(w3)
else:
self.cache[key] = [w3]
def generate_markov_text(self, size=25):
seed = random.randint(0, self.word_size-3)
seed_word, next_word = self.words[seed], self.words[seed+1]
w1, w2 = seed_word, next_word
gen_words = []
for i in xrange(size):
gen_words.append(w1)
w1, w2 = w2, random.choice(self.cache[(w1, w2)])
gen_words.append(w2)
return ' '.join(gen_words)
为了看到一个示例结果，我们从古腾堡计划中拿了沃德豪斯的《My man jeeves》作为文本，示例结果如下。
In [1]: file_ = open('/home/shabda/jeeves.txt')
In [2]: import markovgen
In [3]: markov = markovgen.Markov(file_)
In [4]: markov.generate_markov_text()
Out[4]: 'Can you put a few years of your twin-brother Alfred,
who was apt to rally round a bit. I should strongly advocate
the blue with milk'
[如果想执行这个例子，请下载jeeves.txt和markovgen.py
马尔可夫算法怎样呢？
这是一个示例文本。
这个文本对应的语料库像这样，
{('The', 'quick'): ['brown'],
('brown', 'fox'): ['jumps', 'who', 'who'],
('fox', 'jumps'): ['over'],
('fox', 'who'): ['is', 'is'],
('is', 'slow'): ['jumps'],
('jumps', 'over'): ['the', 'the'],
('over', 'the'): ['brown', 'brown'],
('quick', 'brown'): ['fox'],
('slow', 'jumps'): ['over'],
('the', 'brown'): ['fox', 'fox'],
('who', 'is'): ['slow', 'dead.']}
现在如果我们从"brown fox"开始，接下来的单词可以是"jumps"或者"who"。如果我们选择"jumps"，然后当前的状态就变成了"fox jumps"，再接下的单词就是"over"，之后依此类推。
提示
