Finding links and initiators: a graph reconstruction problem

TL;DR

This paper introduces a graph reconstruction method using MCMC to infer directed links and initiators from binary observation matrices, with extensions for temporal data, applicable to ecological and paleontological datasets.

Contribution

The paper formally defines the link and initiator inference problem and proposes an MCMC framework, extending it to handle temporal sequences of observation matrices.

Findings

Effective in reconstructing links and initiators from real data

Works well with ecological and paleontological datasets

Provides reasonable and practical results

Abstract

Consider a 0-1 observation matrix M, where rows correspond to entities and columns correspond to signals; a value of 1 (or 0) in cell (i,j) of M indicates that signal j has been observed (or not observed) in entity i. Given such a matrix we study the problem of inferring the underlying directed links between entities (rows) and finding which entries in the matrix are initiators. We formally define this problem and propose an MCMC framework for estimating the links and the initiators given the matrix of observations M. We also show how this framework can be extended to incorporate a temporal aspect; instead of considering a single observation matrix M we consider a sequence of observation matrices M1,..., Mt over time. We show the connection between our problem and several problems studied in the field of social-network analysis. We apply our method to paleontological and ecological data and show that our algorithms work well in practice and give reasonable results.