Lecture04 hmms1_2_ evaluation, parsing, posterior decoding, learning, hmm architectures

zying / January 2023

HMM basic, evaluation, parsing, posterior decoding

Observation, Models, Bayes’ rule, Bayesian inference

通过观测每天天气推断所处季节时，observations指的是能够直接观测获取到的数据（每天的天气），可以推断处于某个季节观测到某种天气的概率 该模型构建的目的就是通过P(observation|season) 推断P(season|observation) 可以通过Bayes’ Rule计算得：

Markov Chains and Hidden Markov Models

• 马尔可夫链主要特点是无记忆性，同HMM差别在于所有状态均可以被观测到，不存在隐藏状态
• HMM存在隐藏状态，可以通过observation推断隐藏状态
• 通过HMM detecting GC-rich regions
• HMMs在基因组注释方面有广泛应用：

Calculating joint probability of one (seq, parse) P(x, $\pi$)

• 计算某一条路径的联合概率
• 以全是P，全是B，部分为P序列为例说明
• Joined prob. : $P(X,\pi)=P(X|\pi)P(\pi)=P(emissions|path)\times P(path)$

  Viterbi algorithm (choosing optimal path)

• 类似DP的方法，根据给定状态序列$\pi^*$寻找具有最大total joint prob. 的最优路径$P[X,\pi]$

• 定义$V_k(i)=$Prob. of most likely path through state $!\pi_i=k$

  Forawrd algorithm

Posterior Decoding

Increasing the ‘state’ space/adding memory

Finding GC-rich regions vs. finding CpG islands

Gene structures GENSCAN, chromatin ChromHMM

Learning (ML training, Baum-Welch, Viterbi training)

Supervised

Unsupervised

Conditional Random Fields (CRFs) & dependencies