Mis-Information Removal in Social Networks: Constrained Estimation on Dynamic Directed Acyclic Graphs

A key issue in the multi agent state estimation presented in social networks is the inadvertent multiple re-use of data also known as mis-information propagation or data incest. We formulate this mis-information propagation in a graph theoretic setting and give a necessary and sufficient conditions on the topology of information flow network so that the underlying state can be estimated optimally. A distributed fusion algorithm is proposed so that the social network has incest free estimates. We also provide a discussion on mis-information removal algorithm for information exchange protocols where people learn from actions of others in a social network. A sub-optimal algorithm is also presented when the information flow graph is not known. Numerical examples are provided to illustrate the performance of the proposed optimal and sub-optimal algorithms.