Thank you! I understood what Markov Chains are now. Nicely done and in a simple understandable fashion.
I am also trying to understand what they call Hidden Markov Model (specifically, I just cannot wrap my head around how it gets used in speech. They just look like entirely different things). Would be awesome to see an update with the Hidden MM.
To understand an HMM:
Start with a MM with two states.
In state "A" we always observe "X"
in state "B" we always observe "Y".
That's a basic MM. Now lets change it to a HMM. Now,
in state "A" we observe "X" 90% of the time and "Y" 10% of the time, and
in state B we observe "Y" 90% of the time and "X" 10%.
The observations don't tell us exactly what state we're in. The state is "hidden." We still get a clue about the state, but there is some uncertainty.
A short overview of using HMMs for speech recognition:
Speech is temporal, a speech sample can be represented as a sequence of data points. Thus, a simple way to compare two speech samples can be an algorithm to compare their corresponding sequences. One such algorithm is DTW, which is an equivalent of the Levenshtein distance algorithm for comparing strings.
So now we have a method of comparing two speech samples. Thus, a simple way to recognize an unknown speech sample can be to keep samples of all possible utterances (phonemes, words, sentences) and just return the best match. That’s not possible - so in speech recognition, they only keep samples of phonemes, and try to find the most likely concatenation of them relative to the unknown sample. The search space is huge, but luckily dynamic programming algorithms exist to make the search fast (they’re called Connected Word Recognition algorithms).
The problem with this approach is that it does not scale. There are tons of variations possible for the same spoken unit (different styles and durations). This is where the Hidden Markov Model comes in. A single HMM can be used to represent all variations of that unit. For example, it can be used to represent multiple speech samples of the word “apple”, or of the phoneme “æ” and so on. There are methods for evaluating the similarity of an HMM and a speech sample, and for training an HMM using multiple samples.
You can also connect phoneme HMMs together to get a big HMM representing words/sentences. The same CWR algorithms as before apply.
Imagine that you've got a markov model just like what this article suggests. Now imagine that in each round your markov model emits a state and then sends that state to a noise box which converts that state into some kind of sound.
As a simple model, say S1 leads to a rising C, S2 leads to a falling F, S3 leads to a stable Bb.
In a more complex model, this sound box is actually plays two or three sounds all at once. As a further complexity, many output sounds overlap between states.
If you're a scientist observing just the sounds being made then you're talking about an HMM (because the markov model is "hidden" behind the sound box). We model speech this way by assuming (sort of) that speech is composed of phonemes (each state) which might sort of overlap in their actual sound.
So a scientist using an HMM tries to reverse the process—listen to the sounds and figure out the phonemes that generated it by knowing something about how people make transitions between phonemes in, say, English words.
Suppose the Markov "state" is what word a user just intended to speak. You can use a non-hidden Markov Model to generate sentences.
But for speech-recognition, you don't know what the user said (that's your goal) and you're guessing based on audio sensor data. This means the true state is "hidden" from you, and you're trying to make educated guesses.
Using a Hidden Markov Model allows you to combine your imperfect indicators (audio samples that sound like certain words) with statistical knowledge (how likely certain words are to follow other words) to improve your guesses.
Comments
Thank you! I understood what Markov Chains are now. Nicely done and in a simple understandable fashion.
I am also trying to understand what they call Hidden Markov Model (specifically, I just cannot wrap my head around how it gets used in speech. They just look like entirely different things). Would be awesome to see an update with the Hidden MM.
To understand an HMM: Start with a MM with two states. In state "A" we always observe "X" in state "B" we always observe "Y". That's a basic MM. Now lets change it to a HMM. Now, in state "A" we observe "X" 90% of the time and "Y" 10% of the time, and in state B we observe "Y" 90% of the time and "X" 10%. The observations don't tell us exactly what state we're in. The state is "hidden." We still get a clue about the state, but there is some uncertainty.
This is an excellent explanation, thanks!
A short overview of using HMMs for speech recognition:
Speech is temporal, a speech sample can be represented as a sequence of data points. Thus, a simple way to compare two speech samples can be an algorithm to compare their corresponding sequences. One such algorithm is DTW, which is an equivalent of the Levenshtein distance algorithm for comparing strings.
So now we have a method of comparing two speech samples. Thus, a simple way to recognize an unknown speech sample can be to keep samples of all possible utterances (phonemes, words, sentences) and just return the best match. That’s not possible - so in speech recognition, they only keep samples of phonemes, and try to find the most likely concatenation of them relative to the unknown sample. The search space is huge, but luckily dynamic programming algorithms exist to make the search fast (they’re called Connected Word Recognition algorithms).
The problem with this approach is that it does not scale. There are tons of variations possible for the same spoken unit (different styles and durations). This is where the Hidden Markov Model comes in. A single HMM can be used to represent all variations of that unit. For example, it can be used to represent multiple speech samples of the word “apple”, or of the phoneme “æ” and so on. There are methods for evaluating the similarity of an HMM and a speech sample, and for training an HMM using multiple samples.
You can also connect phoneme HMMs together to get a big HMM representing words/sentences. The same CWR algorithms as before apply.
Imagine that you've got a markov model just like what this article suggests. Now imagine that in each round your markov model emits a state and then sends that state to a noise box which converts that state into some kind of sound.
As a simple model, say S1 leads to a rising C, S2 leads to a falling F, S3 leads to a stable Bb.
In a more complex model, this sound box is actually plays two or three sounds all at once. As a further complexity, many output sounds overlap between states.
If you're a scientist observing just the sounds being made then you're talking about an HMM (because the markov model is "hidden" behind the sound box). We model speech this way by assuming (sort of) that speech is composed of phonemes (each state) which might sort of overlap in their actual sound.
So a scientist using an HMM tries to reverse the process—listen to the sounds and figure out the phonemes that generated it by knowing something about how people make transitions between phonemes in, say, English words.
Suppose the Markov "state" is what word a user just intended to speak. You can use a non-hidden Markov Model to generate sentences.
But for speech-recognition, you don't know what the user said (that's your goal) and you're guessing based on audio sensor data. This means the true state is "hidden" from you, and you're trying to make educated guesses.
Using a Hidden Markov Model allows you to combine your imperfect indicators (audio samples that sound like certain words) with statistical knowledge (how likely certain words are to follow other words) to improve your guesses.