1. Structured prediction
A diák alatti jegyzetszöveget írta: Balogh Tamás Péter
13/04/2016

2. Structured prediction
the sample is not IID anymore
Supervised learning
Instance = structrure
Structure can be
sequence
tree, graph …

3. Applications Speech and natural language processing Image processing
Clinical diagnostics

4. Sequence labeling
Sequence is the simplest structure E.g.: Assign a label to each of the frames about the state of the movement

5. slide copyright of Nicolas Nicolov

6. slide copyright of Nicolas Nicolov

7. slide copyright of Nicolas Nicolov

8. slide copyright of Nicolas Nicolov

9. Hidden Markov Models
(HMM)

10. Hidden Markov Models Discrete Markov Process
There are N states, the system (nature) is in one of the states in every point in time
notes that the state of the system in time point t is Si

11. Hidden Markov Modells
The current state of the system depends exclusively on the previous states
First order Markov Model:

12. Transition probabilities
The transition among states is stacionary, i.e. it does not dependent on the time:
Sequence initial probs:

13. Emission probabilities
The states qt are not observable (hidden). Let’s assume we have access to observable variables of the system. We can observe a single discrete random variable with M possible values:
Emission probabilites:

14. Hidden Markov Models

15. HMM example Stock exchange price forecast
S = {positive, negative, neutral} mood
O = {increasing, decreasing} price

16. Tasks at HMMs λ are known. What is the likelihood of observing i.e.
λ are known. What is the most probable hidden state sequence for an observation sequence (decoder) ?
argmax

17. Evaluation (1.) task
Given λ and , =?

18. Evaluation (1.) task Forward(-backward) algorithm: forward variables:
Time complexity: O(NTT)
Forward(-backward) algorithm:
forward variables:
recursive procedure
initialisation:

19. Forward algorithm
Time complexity: O(N2T)

20. Most probable sequance (decoder)
Given λ and ,
argmax P(Q| λ,O) =?
Viterbi algorithm
Dynamic programming
δt(i) notes the sequence 1..t where qt=Si

21. Viterbi algorithm

22. Hidden Markov Models

23. Discriminative sequence labeling

24. Discriminative sequence labeling
P(D|c)
P(c|D)

25. Discriminative sequence labeling
arbitrary feature set

26. Decoder in discriminative sequence labeling

27. Viterbi for the decoder
initalisation:

28. Maximum Entropy Markov Model MEMM
MEMM is a discriminative seq labeler
A single (Bayesian) classifier is learnt:

29. Conditional Random Fields

31. CRF training
gradient descent-based techniques…

32. Structured perceptron
Online learning
Decoding with the actual parameters
Update if the predicted and expected structures not equal
Update by the difference of the two aggregated feature vectors

33. Structured perceptron
Viterbi decoder is the same! Training (parameter update):

34. Over the sequences...

35. Tree prediction - PCFG

36. Tree prediction – CYK algoritmh

37. Summary Structured prediction tasks Hidden Markov Models
pl. sequence labeling
Hidden Markov Models
Discriminative sequence labelers
(MEMM, CRF, structured perceptron)