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I'm currently looking at this paper about bayesian knwoledge tracing.Though i can understand HMM's and their computations,i Have trouble relating it to the inference formulas for this paper.

Individualized Bayesian Knowledge Tracing Models Michael V. Yudelson, Kenneth R. Koedinger, and Geoffrey J. Gordon.

the exact problem is how to learn the paramters for this model,i know i have to compute aplha,beta probablities and do it using belm-waulch,but i don't understand how can i code this model and what my formulas for infernece would look like,since i can only make out for 600 students i have 600 parameters p(T|S) accounting that transition probabilty is conditioned on student and 2 guess and slip parameters.Now i have two questions

1.How do my inference formulas look like after learning these parameters.(exact formulas would be helpful)

2.How do i code this using EM(baum-welch) i mean the code changes for alpha and beta probabilties.

The major problem is i can't figure out how the conditioning of a mutinomial node on tranisition parameters will affect the code.

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here is an implementation of BKT done by Baker, its in java and I think it will be easier to look at it.

https://pslcdatashop.web.cmu.edu/ExternalTools?toolId=2

the main idea to get is that you will make different networks for different skills. The zip contain the fitting algorithm in java which estimates the parameters for the network, and the doc file which tells you what formulas to use and the papers where they got them from.