You can solve this sort of problem with Infer.NET but you need to decide what your model is.

Assuming I have understood your question correctly, one model would be a probit regression (a Bayes point machine). For each of the 7 attributes you would have an array of weights derived from some prior. Your model would use the GetItem factor to pick out
the correct weight. Then sum the weights, add noise, and threshold at 0 to give a boolean output. At training you would observe which items to get, and the outcomes, and query the model for the weights. At prediction time, you would observe which items to
get, use the weight posteriors as priors, and query the model for the outcomes.

This is just one model. If you know more about your data you might be able to formulate a more customised model.

John