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I have the data about usage of several services in the population and the data about interactions among users.

The idea is to determine, who is user's friend and who has interacted just "accidentally". The basic idea is that friends affect users behavior. So if a friend or a number of friends adopted the service, there is a bigger chance that you will adopt is as well.

Tho probability of service adoption is represented as Bayes Network:

P(FA,GA,UA) = P(FA)P(GA)P(UA|FA,GA) where FA = friend adoption = {Service A, B, C, D} GA = global adoption = {A, B, C, D} UA = observed user adoption = {A, B, C, D} 

Besides the data of service adoption I have the data of users interactions: UserA, UserB, sum(interactions duration), number of interactions

What I would like to do here is determine the optimal values for parameters c, d for logistic regression P(neighbor = friend|number of interactions, duration) = 1/(1+exp(-c*number of interactions - d*duration)) that fits the best the given data of service adoption and Bayes Network.

Does anyone know what would be the best approach for solving the given problem?

Thank you!

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If you are trying to fit your data to the logistic function, the usual method is Maximum Likelihood Estimation of the parameters (in your case c and d). Since a closed-form expression for the ML estimator of the logistic function does not exist, you have to use a numerical method (e.g. Newton). http://en.wikipedia.org/wiki/Logistic_regression#Maximum_likelihood_estimation