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What is the difference between markov chain models and hidden markov model? I've read in Wikipedia, but couldn't understand the differences.
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A Markov chain is a discrete-time process for which the future behaviour, given the past and the present, only depends on the present and not on the past. A Markov process is the continuous-time version of a Markov chain. Many queueing models are in fact Markov processes.
Markov model is a state machine with the state changes being probabilities. In a hidden Markov model, you don't know the probabilities, but you know the outcomes.
The Hidden Markov Model In this model, the observed parameters are used to identify the hidden parameters. These parameters are then used for further analysis. The HMM is a type of Markov chain. Its state cannot be directly observed but can be identified by observing the vector series.
The Hidden Markov model is a probabilistic model which is used to explain or derive the probabilistic characteristic of any random process. It basically says that an observed event will not be corresponding to its step-by-step status but related to a set of probability distributions.
To explain by example, I'll use an example from natural language processing. Imagine you want to know the probability of this sentence:
I enjoy coffee
In a Markov model, you could estimate its probability by calculating:
P(WORD = I) x P(WORD = enjoy | PREVIOUS_WORD = I) x P(word = coffee| PREVIOUS_WORD = enjoy) Now, imagine we wanted to know the parts-of-speech tags of this sentence, that is, if a word is a past tense verb, a noun, etc.
We did not observe any parts-of-speech tags in that sentence, but we assume they are there. Thus, we calculate what's the probability of the parts-of-speech tag sequence. In our case, the actual sequence is:
PRP-VBP-NN
(where PRP=“Personal Pronoun”, VBP=“Verb, non-3rd person singular present”, NN=“Noun, singular or mass”. See https://cs.nyu.edu/grishman/jet/guide/PennPOS.html for complete notation of Penn POS tagging)
But wait! This is a sequence that we can apply a Markov model to. But we call it hidden, since the parts-of-speech sequence is never directly observed. Of course in practice, we will calculate many such sequences and we'd like to find the hidden sequence that best explains our observation (e.g. we are more likely to see words such as 'the', 'this', generated from the determiner (DET) tag)
The best explanation I have ever encountered is in a paper from 1989 by Lawrence R. Rabiner: http://www.cs.ubc.ca/~murphyk/Bayes/rabiner.pdf
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Markov model is a state machine with the state changes being probabilities. In a hidden Markov model, you don't know the probabilities, but you know the outcomes.
For example, when you flip a coin, you can get the probabilities, but, if you couldn't see the flips and someone moves one of five fingers with each coin flip, you could take the finger movements and use a hidden Markov model to get the best guess of coin flips.
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