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I don't understand how this works. Help would be really appreciated.

Let's say we have a 10 second sound input, we make a feature vector every 10ms - so we have 1000 vectors - $\mathbf{o}=o_1, \cdots,o_{1000}$.

For simplicity, let's say that all we want to know, is what sequence of phones $p=p_1,\cdots,p_n$ is the answer to $\text{argmax } P(o|p)$ for $p$, or at least what's a good estimate/close answer. For all phones, we have a seperate left to right HMM model (I think that's what makes sense in this scenario).

How exactly is this done? Will similar enough vectors be "put together" and only treated as 1? The input is probably not one phone or a thousand phones - but we don't know that... so for what $p$ will $P(o|p)$ be computed?

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Will similar enough vectors be "put together" and only treated as 1?

No, this is not how it is done.

so for what p will P(o|p) be computed?

Your assumption that recognition is performed by considering one by one all possible phone or word sequences and scoring them is wrong. For just a few seconds of speech the number of possible words would be extremely large! This approach - scoring each candidate model among the entire space and picking up the one with the largest score, is actually used only for some small vocabulary / single-word applications (say recognizing several options on a voice menu). I think this confusion stems from the fact that the classic Rabiner tutorial on HMM makes a lot of sense for finite-vocabulary applications, but stays away from all the difficulties/technicalities of continuous applications.

In continuous speech recognition there are several layers on top of the phones models. Phone models are joined together to form words models, and words models are joined together to form a language model. The recognition problem is formulated as searching the path of least cost through this graph.

One could do the same by piecing together HMMs, though... Let's take a simpler example... You have 5 phones and you want to recognize any sequence of them (no words models, no language models - let's consider meaningless speech for this example). You train one left-right HMM per phone, say 3 or 4 states - maybe on clean individual recordings of each phone. To perform continuous recognition, you build a big HMM by adding transition states between the last state of each phone and the first state of each phone. Performing recognition with this new model is done by finding the most likely sequence of states given the sequence of observation vectors - with the Viterbi algorithm. You will know exactly which sequence of states (and thus phones) is the most compatible with the observation. Practically, things are never done this way, and this is why I downplayed in my previous reply the importance of Rabiner's "problem 2": in a true continuous application, the size of the vocabulary is such that considering this giant HMM made of all possibles connections between phones to make words, and words to make sentences would make the naive use of the Viterbi algorithm impossible. We stop reasoning in terms of HMM and we start thinking in terms of FST.

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  • $\begingroup$ With isolated word recognition for finite set of words, you can simply create a HMM model for each word, then you can take maximum of P(O|M). In continuous speech recognition, you do not know how long the sequence of recognizable sounds will be - you piece together HMM models, to make one big HMM model, but by what method can it be determined how good this big HMM model is? Do you in some way still try to get a good P(O|M), where M is this big HMM model, just like with the isolated word recognition? $\endgroup$ – Jake1234 Aug 24 '14 at 15:13
  • $\begingroup$ The thing I don't get - you're mentioning the viterbi algorithmm - so does P(O|M) even matter? Or the two are correlated? If you know the most probable sequence of states for a given big HMM model (of connected HMM models of phones), how does that tell you whether this big HMM model is better than some other big HMM model? Which is what you're going for right? A big HMM model of connected HMM models, that make the observation of 1000 vectors likely. $\endgroup$ – Jake1234 Aug 24 '14 at 15:18
  • $\begingroup$ In a continuous application there is only one big HMM - which describe the entire space of inputs to recognize. So the value of P(O|M) doesn't matter because there's nothing to compare it with. What matters is the sequence of state. $\endgroup$ – pichenettes Aug 24 '14 at 15:24
  • $\begingroup$ 5 Phones, 3-state left-right HMM for each phone. If you'd want to do isolated phone recognition, you could just pick such HMM model, that P(O|M) is the highest, correct? If you want to recognize a sequence of phones, and connect HMM phone models together for a big HMM, would you not want a high P(O|M)? How will the state sequence tell you if the big HMM model is connected out of the right phone HMM models? If you want to use the viterbi algorithm, I can only imagine using a fully connected HMM model (not left-right), where each state is a phone, or something like that. Is that what you mean? $\endgroup$ – Jake1234 Aug 24 '14 at 19:03
  • $\begingroup$ "How will the state sequence tell you if the big HMM model is connected out of the right phone HMM models?". There is only one HMM model so there's no way of getting it wrong. There's no alternative. You're not discriminating between several model. There is only one model, and finding the path through it tells you what your input is. $\endgroup$ – pichenettes Aug 24 '14 at 19:12

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