Hidden Markov Models: The Backbone of Traditional Speech Recognition
Pascual Vila
AI & Audio Processing Instructor // Code Syllabus
Before the era of deep neural networks like Wav2Vec, Hidden Markov Models (HMMs) were the undisputed kings of speech processing. By combining statistical probabilities with dynamic programming, HMMs allowed computers to understand human voice.
States and Observations
In a Hidden Markov Model, we assume the system we are modeling is a Markov process with unobserved (hidden) states. In speech to text, what we actually hear (the audio waveform, converted into MFCCs) are the Observations. The actual phonemes or words the speaker is saying are the Hidden States.
The goal of the HMM is to look at the sequence of observations and deduce the most likely sequence of hidden states that produced them.
Two Types of Probabilities
- Transition Probabilities: The probability of moving from state A to state B. For example, in English, the phoneme /t/ is highly likely to transition to /h/ (forming "th"), but very unlikely to transition to /x/.
- Emission Probabilities: The probability that a specific hidden state (e.g., /s/) will produce a specific observation (e.g., high-frequency hissing audio). Gaussian Mixture Models (GMMs) were traditionally used to model these continuous acoustic emissions.
The Viterbi Algorithm
Once an HMM is trained (usually via Expectation-Maximization / Baum-Welch), we use it to decode new audio. Because testing every possible path of phonemes would take billions of years, we use the Viterbi algorithm. Viterbi uses dynamic programming to discard unlikely paths on the fly, finding the single most probable sequence of hidden states in a fraction of a second.
❓ Core HMM Queries
What is the difference between an HMM and a standard Markov Chain?
In a standard Markov Chain, the states are directly visible to the observer, meaning the state transition probabilities are the only parameters. In a Hidden Markov Model, the states are not directly visible; instead, we only see the outputs (emissions) dependent on the states.
How is hmmlearn used for Speech Recognition in Python?
`hmmlearn` provides an object-oriented API for HMMs. Typically, you instantiate a `GaussianHMM` to handle continuous acoustic data.
from hmmlearn import hmm
model = hmm.GaussianHMM(n_components=3)
model.fit(mfcc_audio_features) # Training
states = model.decode(new_mfcc) # Viterbi prediction