隱式馬爾科夫模型HMM - Lecture Note for CS188(暨CS181 ShanghaiTech)

說明：筆記旨在整理我校CS181課程的基本概念(PPT借用了Berkeley CS188)。由於授課及考試語言爲英文，故英文出沒可能。

目錄

 

1 Markov Models(aka Markov chain/process)

2 Hidden Markov Models

3 Inference tasks

4 Dynamic Bayes Nets

5 Particle Filtering

Reference

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1 Markov Models(aka Markov chain/process)

1.state: value of X at a given time

2.transition model:  specifies how the state evolves over time.

3.stationarity assumption:  same transition probabilities at all time steps

4. markov assumption(first order):  

5. stationary distribution: 

2 Hidden Markov Models

 Hidden Markov models (HMMs)

① Underlying Markov chain over states X. ② You observe E at each time step.

It is well defined by: ① Initial distribution: . ② Transition model: . ③ Emission model: 

Its joint distribution: 

3 Inference tasks

1.State trellis（狀態框架）

2. Filtering: 

3. Most likely explanation: 

Example:

4 Dynamic Bayes Nets

1. Dynamic Bayes Nets(DBN): represents a first-order Markov process so that each variable can have parents only in its own slice or the immediately preceding slice(aka time slice).

2.  Every HMM is a single-variable DBN / Every discrete DBN can be represented by a HMM.

3. Adavantage of HMM: sparse dependencies => exponentially fewer parameters

5 Particle Filtering

1. Represent belief state at each step by a set of samples(called particles).

P(X) is now a list of N particles, approximated by number of particles

2. Propagate forward: 

3. Observe: 

4. Resample: Genearte N new samples from weighted sample ditriution

Reference

1. Artificial Intelligence, A Modern Approach. 3rd Edition. Stuart R., Peter N. Chapter 15

2. CS 188: Artificial Intelligence Hidden Markov Models