At least one embodiment of this disclosure includes a method of inferring attribute labels for a user in a social networking system based on the user's social connections and user-specified attribute labels in the social networking system. The method can include: establishing variational equations based on attribute labels of nodes in an ego network in a social graph of a social networking system; determining likelihood scores for at least a portion of the attribute labels of neighboring nodes from a focal user node in the ego network based on user-specified attribute labels from the social networking system; and calculating probability distributions of possible attribute labels for the focal user node of the ego network based on the variational equations and the likelihood scores.
Please help me write a proper abstract based on the patent claims. CLAIM: 1-15. (canceled) 16. A computer-implemented method, comprising: establishing variational equations based on attribute labels of nodes in an ego network in a social graph of a social networking system; determining likelihood scores for at least a portion of the attribute labels of neighboring nodes from a focal user node in the ego network based on user-specified attribute labels from the social networking system; computing probability distributions of possible attribute labels for the focal user node of the ego network based on the variational equations and the likelihood scores; and providing at least a portion of the computed probability distributions with an external process instance inferring labels for another ego network of the social networking system. 17. The computer-implemented method of claim 16, further comprising: receiving an update to a first attribute label of at least one of the neighboring nodes, wherein the update is a user-reported attribute label or a probability distribution update of possible attribute labels from the external process instance inferring labels for another ego network of the social networking system; and re-calculating re-computing the probability distributions based at least partly on the update. 18. The computer-implemented method of claim 16, further comprising: inferring an attribute label based on the probability distributions for the focal user node; and generating a user prompt based on the inferred attribute label for advertisement, friend suggestion, label suggestion, or affiliation suggestion. 19. The computer-readable storage medium of claim 16, wherein computing the probability distribution includes inferring an explanation for a formation of a social connection in the ego network. 20. A computer system, comprising: a component configured to establish variational equations based on attribute labels of nodes in a first ego network in a social graph of a social networking system; a component configured to set likelihood scores for at least a portion of the attribute labels of neighboring nodes from a focal user node in the ego network based on user-specified attribute labels from the social networking system; a component configured to compute probability distributions of possible attribute labels for the focal user node of the ego network based on the variational equations and the likelihood scores; and a component configured to share at least a portion of the computed probability distributions with another process instance of a method inferring labels for a second ego network of the social networking system. 21. The system of claim 20, further comprising: a component configured to receive an update to a first attribute label of at least one of the neighboring nodes, wherein the update is a user-reported attribute label or a probability distribution update of possible attribute labels from an external process instance configured to infer labels for another ego network of the social networking system; and a component configured to re-compute the probability distributions based at least partly on the update. 22. The system of claim 20, further comprising: a component configured to infer an attribute label based on the probability distributions for the focal user node; and a component configured to generate a user prompt based on the inferred attribute label for advertisement, friend suggestion, label suggestion, or affiliation suggestion. 23. The system of claim 20, wherein computing the probability distribution includes inferring an explanation for a formation of a social connection in the ego network. 24. A non-transitory computer-readable medium storing instructions, the instructions comprising: instructions for establishing variational equations based on attribute labels of nodes in an ego network in a social graph of a social networking system; instructions for determining likelihood scores for at least a portion of the attribute labels of neighboring nodes from a focal user node in the ego network based on user-specified attribute labels from the social networking system; instructions for computing probability distributions of possible attribute labels for the focal user node of the ego network based on the variational equations and the likelihood scores; and instructions for providing at least a portion of the computed probability distributions with an external process instance inferring labels for another ego network of the social networking system. 25. The computer-implemented method of claim 24, further comprising: instructions for receiving an update to a first attribute label of at least one of the neighboring nodes, wherein the update is a user-reported attribute label or a probability distribution update of possible attribute labels from the external process instance inferring labels for another ego network of the social networking system; and instructions for re-computing the probability distributions based at least partly on the update. 26. The computer-implemented method of claim 24, further comprising: instructions for inferring an attribute label based on the probability distributions for the focal user node; and instructions for generating a user prompt based on the inferred attribute label for advertisement, friend suggestion, label suggestion, or affiliation suggestion. 27. The computer-readable storage medium of claim 24, wherein the instructions for computing the probability distribution include instructions for inferring an explanation for a formation of a social connection in the ego network.