Modeling and Predicting Co-Occuring Values I have data for a 100,000 people with different personality traits. Here would be sample data:

Person  Trait-1   Trait-2   Trait-3 .....   Trait-N
John     1          0         1                1


I need a model where for a new user when I see Trait-X, I need a prediction of the likelihood of all other Traits i.e. how likely is he to have any of the other traits. Can someone point me to a possible model I could use? I am a novice so don't know much about this space.
I would recommend a Restricted Boltzmann machine, which is a type of neural network that can model probability distributions. What you are trying to do is to estimate the marginal distribution of the missing features. In a probabilistic model, this is done through marginalization. The beauty of this method is that it provides the full distribution over the missing features rather than mere point estimates.

Here are two tutorials.