ECS170-L23

📗 -> 05/21/25: ECS170-L23

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Lecture Slide Link

🎤 Vocab

❗ Unit and Larger Context

came in 30 mins late…

HMM Problems

1. Likelihood - Hidden states?
2. Decoding - Likelihood of next state?
3. Learning - Finding underlying HMM model from observations

✒️ -> Scratch Notes

Viterbi Algorithm vs Forward Algorithm

Identical, except:

• Viterbi takes the max over the previous path probabilities, whereas the forward algorithm takes the sum.
• Viterbi algorithm has one component that the forward algorithm doesn’t have: backpointers.
  • forward algorithm only needs to produce an observation likelihood
  • Viterbi algorithm must produce a probability and also the most likely state sequence
  • We compute this best state sequence by keeping track of the path of hidden states that led to each state, and then at the end backtracing the best path to the beginning (the Viterbi backtrace)

Problem 3. Learning

How to find underlying HMM model (Initial Probability, Transition Probability, Emission Probability) to fit this data?

• Use the forward-backward algorithm or the Baum-Welch algorithm
  • Special case of the expectation maximization algorithm. An iterative algorithm, slowly improving learned probabilities
    • maximum likelihood estimation (MLE)

Picture taken ->
forward backward algorith

• Initialize A and B
• Iterate until convergence

• E-Step (expectation)

• M-Step (maximization)
  • Apply the variables calculated in E-step to maximize expectation

🧪 -> Refresh the Info

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🔗 -> Links

Resources

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Connections

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