The Hidden Markov Model
A Markov chain is useful when we need to compute a probability for a sequence of observable events. In many cases, however, the events we are interested in are hidden hidden: we don’t observe them directly. For example we don’t normally observe part-of-speech tags in a text. Rather, we see words, and must infer the tags from the word sequence. We call the tags hidden because they are not observed.
- $B=b_i(o_t)$,表示为在 $i$ 状态下，会观测到 $o_t$ 的概率
Hidden Markov Model举例
Imagine that you are a climatologist in the year 2799 studying the history of global warming. You cannot find any records of the weather in Baltimore, Maryland, for the summer of 2020, but you do find Jason Eisner’s diary, which lists how many ice creams Jason ate every day that summer. Our goal is to use these observations to estimate the temperature every day. We’ll simplify this weather task by assuming there are only two kinds of days: cold (C) and hot (H).