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Feature Request: HMM Inference #20

Open GoogleCodeExporter opened 9 years ago

GoogleCodeExporter commented 9 years ago 
What steps will reproduce the problem?
1.
2.
3.

What is the expected output? What do you see instead?
I would like to see the exposure of the backward and forward algorithms to the 
CLI for HMM inference, including determine the backward, forward and posterior 
probabilities of states given sequence symbol, as the 
backward/forward/posterior function in the R's HMM package (see link below).

What version of the product are you using? On what operating system?
0.6.1; Windows 7

Please provide any additional information below.
http://cran.r-project.org/web/packages/HMM/HMM.pdf

Original issue reported on code.google.com by changzho...@gmail.com on 18 Jul 2011 at 6:06

GoogleCodeExporter commented 9 years ago 
Indeed, given the input HMM model with N+1 states S_0,...N, and an input 
observation sequence of M+1 symbols O_0,...,O_m:

The probability for the state at time t, q[t], to be equal to S_i can be 

ForwardProbability(q[t]==S_i|O_0,...,O_t) = alpha[t][i]/(sum_{j=0..N} 
alpha[t][j])
BackwardProbability(q[t]=S_i|O_{t+1},...,O_m) = beta[t][i]/(sum_{j=0..N} 
beta[t][j])
PosteriorProbability(q[t]=S_i|O_0,...,O_m) = 
alpha[t][i]*beta[t][i]/(sum_{j=0..N} alpha[t][j]*beta[t][j])

This can be easily implemented in the HMM class.

Original comment by changzho...@gmail.com on 19 Jul 2011 at 3:51