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# Learning Objectives - Apply HMMs to speech recognition - Understand training (Baum-Welch) and decoding (Viterbi) - Model subword units (phonemes) - Probability and Markov chains - Week 3: MFCC features ## 1. HMMs for Speech HMMs model speech as sequence of hidden states (phonemes) that produce observable acoustic...
Learning Objectives
- Apply HMMs to speech recognition
- Understand training (Baum-Welch) and decoding (Viterbi)
- Model subword units (phonemes)
- Probability and Markov chains
- Week 3: MFCC features
1. HMMs for Speech
HMMs model speech as sequence of hidden states (phonemes) that produce observable acoustic features (MFCCs).
Components:
- States: Typically 3-5 states per phoneme (beginning, middle, end)
- Observations: MFCC vectors (continuous, modeled by Gaussian Mixture Models)
- Transitions: Probability of moving between states
- Initial: Probability of starting in each state
2. Three Problems
- Evaluation (Forward algorithm): P(O|model) - how likely is observation given model?
- Decoding (Viterbi algorithm): Find most likely state sequence given observation
- Training (Baum-Welch/EM): Learn model parameters from training data
3. Acoustic Modeling
Context-Dependent Phonemes: Triphones (phoneme with left and right context). Handles coarticulation (sounds change based on neighbors). Increases model count from ~50 to thousands.
Tied States: Share acoustic observations across similar states. More robust estimation with limited data.
Language Model Integration: Combine acoustic model (P(X|W)) with language model (P(W)):
Q1: Why use HMMs for speech recognition?Speech is sequential (temporal) and variable in duration (speed). HMMs naturally model: sequential structure (states = parts of phoneme), variable duration (self-transition loops), and probabilistic nature of speech. Q2: What is the Viterbi algorithm used for in ASR?Find the most likely sequence of words/phonemes given acoustic observations. Dynamic programming algorithm that efficiently searches through state space. Used during recognition (decoding). Q3: What are triphones and why are they needed?Context-dependent phoneme models: phoneme with preceding and following context (e.g., "k" in "ski" vs "cool"). Captures coarticulation effects where phoneme acoustics change due to neighboring sounds. Q4: What is the role of the language model in ASR?P(W) = probability of word sequence. Helps disambiguate acoustically similar phrases ("recognize speech" vs "wreck a nice beach"). Typically n-gram models (word sequences of length n). Q5: What is the Baum-Welch algorithm?Expectation-Maximization (EM) algorithm for learning HMM parameters from unlabeled training data. E-step: compute expected state occupations given current parameters. M-step: update parameters to maximize expected likelihood. Q6: How are GMMs used with HMMs in speech?Each HMM state uses a Gaussian Mixture Model (GMM) to model the probability of observing acoustic features in that state. GMM captures variability in speech (different speakers, speaking styles, contexts). Join Discord PreviousSpeech Analysis & FeaturesNextGaussian Mixture Models & Acoustic Modeling