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HIDDEN MARKOV MODEL

Group 1: Nguyễn Đức Phước Lê Trung HiếuVõ Hồng Phúc

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December 19th, 2014 10/22/2022Group 1 - Nguyễn Đức Phước - Lê Trung Hiếu - Võ Hồng Phúc - HMM & Application

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10/22/2022Group 1 - Nguyễn Đức Phước - Lê Trung Hiếu - Võ Hồng Phúc - HMM & Application 2

Out lineIntroduction

Hidden Markov Model – HMMIndependent Assumptions Elements of An HMMThe Three Basic probem for HMMs

Evaluating Problem – Forward AlgorithmSolving ProblemMatlab Implementation

Decoding Problem – Virtebi Algorithm Baum – Welch Algorthm

Application


Introduction Hidden Markov Model – HMM Application

Introduction



Hidden Markov Model – HMMIndependent Assumptions Elements of An HMMThe Three Basic probem for HMMs



Application



Hidden Markov Model – HMMIndependent Assumptions Elements of an HMMThe Three Basic probem for HMMs



Application


Hidden Markov Model – HMMWhat‘s an HMMIntroduction Application

What’s an HMM

Graphical ModelCircles indicate statesArrows indicate probabilistic dependencies between states



What’s an HMM

Green circles are hidden statesDependent only on the previous state“The past is independent of the future given the present.”



What’s an HMM

Purple nodes are observed statesDependent only on their corresponding hidden state



Hidden Markov Model – HMMWhat’s an HMM?Elements of an HMM The Three Basic probem for HMMs



Application


Hidden Markov Model – HMMElements of An HMMIntroduction Application

HMM FormalismA

B

AAA

BB

NNN

MMM

N

M

N

M

{N, M, P, A, B} M : The number of distinct observation symbols per state, i.e., the discrete alphabet size.

N : The number of states in the states in the model. P = {pi} are the initial state probabilitiesA = {aij} are the state transition probabilitiesB = {bik} are the observation state probabilities



HMM FormalismA

B

AAA

BB

NNN

MMM

N

M

N

M

{N, M, P, A, B} N : The number of states in the states in the model.

Individual states S : {s1…sN } are the values for the hidden states

qt : the state at time t



HMM FormalismA

B

AAA

BB

NNN

MMM

N

M

N

M

{N, M, P, A, B} M : The number of distinct observation symbols per state, i.e., the discrete alphabet size. Individual symbols V : {v1…vM } are the values for the observations



HMM FormalismA

B

AAA

BB

NNN

MMM

N

M

N

M

{N, M, P, A, B} A = {aij}: the state transition probabilities where