Dear  Aman,

In my opinion Matlab is a good software platform for implementing HMM.

At least, as an electrical engineering faculty member, I am very much comfortable with it.

For HMM, there are Matlab toolboxes which can be downloaded free of charge via Internet. For example, you can take a look at the following address:

http://www.cs.ubc.ca/~murphyk/Software/HMM/hmm.html

The above address also includes a list of existing Matlab HMM toolboxes.

In addition, Statistics and Machine Learning Toolbox of Matlab includes some ready functions related to hidden Markov models. These are:

• hmmgenerate — Generates a sequence of states and emissions from a Markov model
• hmmestimate — Calculates maximum likelihood estimates of transition and emission probabilities from a sequence of emissions and a known sequence of states
• hmmtrain — Calculates maximum likelihood estimates of transition and emission probabilities from a sequence of emissions
• hmmviterbi — Calculates the most probable state path for a hidden Markov model
• hmmdecode — Calculates the posterior state probabilities of a sequence of emissions

Best of luck,

Respected Sir (O. Akay),

Thanks for the reply.

As, I am just a beginner. Kindly tell me should I go with per-defined functions in Statistics and Machine Learning Toolbox or with the HMM packages available at the link.   

Hi again Aman,

In my opinion, for getting started, statistics and machine learning commands should  be enough. Bu after having some experience, you might need to go to an HMM  toolbox.

Best whishes,

Alright Sir,

Thanks...

Respected Researchers,

Is their any limit to the total number of observation we should mention in the emission probability table in HMM or we can not down as many observation as we can, just the sum of all observations probabilities should be one. 

Dear Aman,

The following example might answer your question:

Consider two friends, Alice and Bob, who live far apart from each other and who talk together daily over the telephone about what they did that day. Bob is only interested in three activities: walking in the park, shopping, and cleaning his apartment. The choice of what to do is determined exclusively by the weather on a given day. Alice has no definite information about the weather where Bob lives, but she knows general trends. Based on what Bob tells her he did each day, Alice tries to guess what the weather must have been like.

Alice believes that the weather operates as a discrete Markov chain. There are two states, "Rainy" and "Sunny", but she cannot observe them directly, that is, they are hidden from her. On each day, there is a certain chance that Bob will perform one of the following activities, depending on the weather: "walk", "shop", or "clean". Since Bob tells Alice about his activities, those are the observations. The entire system is that of a hidden Markov model (HMM).

Alice knows the general weather trends in the area, and what Bob likes to do on average. In other words, the parameters of the HMM are known. They can be represented as follows in the Python:

states = ('Rainy', 'Sunny')

observations = ('walk', 'shop', 'clean')

start_probability = {'Rainy': 0.6, 'Sunny': 0.4}

transition_probability = {

'Rainy' : {'Rainy': 0.7, 'Sunny': 0.3},

'Sunny' : {'Rainy': 0.4, 'Sunny': 0.6},

}

emission_probability = {

'Rainy' : {'walk': 0.1, 'shop': 0.4, 'clean': 0.5},

'Sunny' : {'walk': 0.6, 'shop': 0.3, 'clean': 0.1},

}

In this piece of code, start_probability represents Alice's belief about which state the HMM is in when Bob first calls her (all she knows is that it tends to be rainy on average). The particular probability distribution used here is not the equilibrium one, which is (given the transition probabilities) approximately {'Rainy': 0.57, 'Sunny': 0.43}. The transition_probability represents the change of the weather in the underlying Markov chain. In this example, there is only a 30% chance that tomorrow will be sunny if today is rainy. The emission_probability represents how likely Bob is to perform a certain activity on each day. If it is rainy, there is a 50% chance that he is cleaning his apartment; if it is sunny, there is a 60% chance that he is outside for a walk.

Dear Olcay,

First of all thanks for replying. But what i want to clarify is that like here we do have observations like "walk", "shop" and "clean". So can we have any number of observations or there should be certain limit to the total number of observations and does the number of observations affects the results in any way. 

I do not think there is a limit for the number of observations (such as  "walk", "shop", and "clean" ), as long as their probabilities add up to 1.

Thanks

Dear Olcay

which HMM software are available? i mean the tools