# I don't understand clearly differences between posterior(of likelihood) ,confidence score and acoustic cost

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### 권해용

Aug 20, 2017, 9:19:25 PM8/20/17
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Hi,
I'm trying to get a probability(like posterior, likelihood) for each arc,
and compare its probability to other phones's one.

Also, I want to know how to get the probability for each frame.

What probability should I use in kaldi?

I converted lattice file to posterior file using lattice-to-post.
The posterior file looked like this:

[27 1] [27 1] [27 1] [27 1] [27 1] [27 1] [27 1] [27 1] [27 1] ...

I already knew the '1' means posterior,
but there were some pages saying it is a 'confidence score'.

acoustic cost,
likelihood,
posterior,
and confidence score.

Now I'm confused what I know about.

### Daniel Povey

Aug 21, 2017, 1:35:28 AM8/21/17
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perhaps someone else can reply to this, I don't have time.
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### Nickolay Shmyrev

Aug 21, 2017, 4:37:30 AM8/21/17
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Hi

Before starting a research like this it is better to get a solid background in theory, otherwise it will be hard for you to develop a proper algorithm. A textbook like "Spoken Language Processing: A Guide to Theory, Algorithm, and System Development" by
or HTK book or any modern course on speech recognition could help you here. A good understanding of probability theory and machine learning in general is also helpful.

Likelihood, usually "acoustic likelihood" is a probabilistic term which describes the probability of a particular observation in the model space. It is basically the probability of a certain observation in a space of training data. Sometimes this probability is not normalized to 1, that is why it is called "likelihood", not "probability".  Basically consider all training data and think how frequently you see something similar to the current observation. This is usually pretty small value.

Acoustic cost is usually the same as "likelihood" but it more relates to the actual value computed in software which might be adjusted by normalization factor or somehow rounded for faster computation. Usually you say "acoustic cost" when you discuss the values of the software variables, dropping their probabilistic nature and considering only the best path search in a graph.

Posterior probability is a measure in posterior space. When you already see the observation you can compare the outcome with all other possible outcomes and compute how probable already observed value. This is a bayesian theory term which can also be computed as a factor between model probability of observation (likelihood) and model probability all other observations (also likelihoods). This value is usually pretty high compared to model probability and basically tells you how certain you are in a model decision.

Since posterior probability is a certainty measure, you can call it a "confidence score" and usually posterior probabilities are used as confidence scores. However, not all confidence scores are probabilistic. For example, you can adjust score with an estimate of expected time or somehow penalize it depending on the time of arrival not considering probabilistic nature. That would also be a "confidence score" but since it is not within probabilistic framework it is not "posterior" anymore. So "confidence score" is more software related term generalizing posterior probability.