Importance Sampling Techniques for Sequentially Choosing Interventions When Reconstructing Directed Networks

• Activity Number: 502
• Type: Contributed
• Date/Time: Wednesday, August 12, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Computing
• Author(s): James Henderson* and George Michailidis
• Companies: University of Michigan and University of Florida
• Keywords: networks ; MCMC ; importance sampling ; DAG ; sequential design

Abstract

Networks representations play an important role in understanding complex systems and reconstructing unknown networks from data is an active area of research. Intervention data can be used to learn directed networks, often formally represented as DAGs. In this talk I begin by presenting a framework for sequentially choosing interventions. I then turn to techniques for addressing the computational challenge of estimating the proposed improvement function, taken to be the entropy of certain posterior marginals. Working with the posterior distribution is difficult in network models due to the combinatorial complexity and discrete nature of DAG-space. It is known that MCMC methods for sampling DAGs mix slowly, but order sampling has been shown to improve mixing. Order sampling constructs a Markov Chain over linear orderings, from which DAGs can then be sampled. Methods for correcting the bias this introduces have also been studied. We build on this work by showing how to construct an importance sample using the hierarchy among linear orders, partial orders, and DAGs. We also show that the bias correction can be directly estimated from the sampled orders.