HMMs

1. HMMs

2. Database text speech text text text Scoring

3. Variability in Speech Signals • Context-Dependent Variability • Style Variability • Speaking rate, Emotional changes, Whispering, shouting • Speaker Variability • Environment Variability

4. The variability affect the time-frequency function or more generally the time-feature function. • Therefore, the acoustic model should be able to represent this variability.

5. Dynamic programming, known as Dynamic Time Warping (DTW) in Speech Recognition can model the speaker rate variability. • However, DTW is not good way to model speaker feature variations (I.e. inter-speaker variation when pronouncing a phoneme). • A better model for tackle this two kind of variability is a HMM.

6. HMMs in Speech Recognition

7. HMMs in Speech Recognition • Introduction • HMM Basics • Isolated Word Recognition • Evaluation P(O/M) • Training • D-HMM • CD-HMM • Continuous Word Recognition

8. HMMs • HMM Basics • Architecture • Observable Markov Model • Hidden Markov Model • Continuous HMM

9. Arquitecture transitions states

10. Observable Markov Model The observations is enough to know which state the system is. In other words, every state has a defined output. Raining Cloudy Transition Matrix Sun

11. HMM The observations you DON´T exactly know which state the system is. Every state output has a set of possibilities, which can be modeled with a pdf. Two coin modeling. Transitions from one state to other means we change the coin. This state represents one coin. This state represents one coin Any coin can be either Tail of Head with this distribution. This is a possible state sequence.

12. We ask a person to take balls of any URN. All URNs have all colors. HMM Modelling Every URN as a different distribution of colors. …

13. In this case, every state in each state is exactly the same color. Therefore, if it enough to use a Discrete Probability function and the Model is Called A Discrete Hidden Markov Model.

14. weight length Continuous Density

15. In this case: • Assuming the observations vectors are not correlated:

16. In this case, every speech component is modeled as a one dimensional Gaussian distribution: • and we calculate:

17. Sometimes, the Gaussian Distribution is not very good distribution model: • In this case a mixture of Gaussians can be used:

18. Three types of animals weight Pigs dogs sheeps length

19. weight length From top

20. Three persons given sizes lenghts and weights of dogs, sheeps and pigs. HMM Modelling All persons can give weight and lengths of all three kind of animalos weight weight length length length weigth

21. This is called a Continuous Density Hidden Markov Model.

22. Continuos Ditribution->Discrete Distribution • We can convert a Continuous Distribution to a Discrete Probability Function. • In order to do this, we first • Classify the data (minimum distance to all classes) • Calculate the probability of the Class.

23. weight length X is class 1 (Pig) x

24. weight length X is class 2 (Sheep) x

25. Probability of each Class HMM Modeling All persons can give weight and lengths of all three kind of animals

26. The process of transforming a Continuous Density function into a Discrete Density function is call Vector Quantization. • If we first classify the observation, we can use D-HMM. • This is convenient to minimise space and computation.

27. Vector Quantisation (VQ) • Convert an infinite number of parametric vectors to a finite set of vectors. • Each speech vector is assigned a new vector (codeword). Choosen from a codebook, using: • In fact, every vector can be represented by a value k, which is the index of the codeword closer to the vector. codeword codebook

28. Transition Probabilities Final state Initial State 1 2 3 4 N-1 N Internal States Internal states has the probability of emitting a vector. Left-right HMM Architecture Finite State Networks, which consist of

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