1. CHAPTER 8 DISCRIMINATIVE CLASSIFIERS HIDDEN MARKOV MODELS

2. Generative vs. Discriminative

3. The Perceptron Model

4. Example: Spam

5. Binary Decision Rule

6. Online Perceptron Training

7. Perceptron Training Illustration

8. Properties of Perceptrons

9. Issues with Perceptrons

10. Reasoning over Time Often, we want to reason about a sequence of observations Speech recognition Robot localization User attention Need to introduce time into our models Basic approach: hidden Markov models (HMMs) More general: dynamic Bayes’ nets

11. Markov Models

12. Conditional Independence

13. Weather Example

14. Mini-Forward Algorithm

15. Example

16. Stationary Distributions If we simulate the chain long enough: What happens? Uncertainty accumulates Eventually, we have no idea what the state is! Stationary distributions: For most chains, the distribution we end up in is independent of the initial distribution Called the stationary distribution of the chain Usually, can only predict a short time out

17. Example: Web Link Analysis

18. Mini-Viterbi Algorithm

19. Hidden Markov Models

20. Example

21. Conditional Independence

22. HMM Applications

23. Forward Algorithm

24. Viterbi Algorithm

25. Viterbi Example

26. Viterbi Properties Designed for computing the most likely state hidden sequence given a sequence of observations in Hidden Markov Models Two passes, forward to compute the forward probabilities, and then backward to reconstruct the maximum sequence What’s the time complexity? O(d2n) - Why is this exciting? There are many extensions to the basic Viterbi algorithm which have been developed for other models which have similar local structure: syntactic parsing, for instance.

27. Speech in an Hour

28. HMMs for Speech

29. HMMs for Continuous Obs.? Before: discrete, finite set of observations Now: spectral feature vectors are real-valued! Solution 1: discretization Solution 2: continuous emissions models Gaussians Multivariate Gaussians Mixtures of Multivariate Gaussians A state is progressively: Context independent subphone (~3 per phone) Context dependent phone (=triphones) State-tying of CD phone

30. ASR Lexicon: Markov Models

31. Viterbi with 2 Words + Unif. LM

32. Conclusion Perceptron A discriminative model, an alternative to generative models like Naïve Bayes Simple classification rule, based on a weight vector Simple online learning algorithm, guaranteed to converge if training set is separable Hidden Markov Models A special kind of Bayesian Network designed for reasoning about sequences of hidden states Polynomial time inference for most likely state sequence (Viterbi) and marginalization (Forward- Backward) Many applications