title: Learning Minimal Latent Directed Information Polytrees.
abstract: We propose an approach for learning latent directed polytrees as long as there exists an appropriately defined discrepancy measure between the observed nodes. Specifically, we use our approach for learning directed information polytrees where samples are available from only a subset of processes. Directed information trees are a new type of probabilistic graphical models that represent the causal dynamics among a set of random processes in a stochastic system. We prove that the approach is consistent for learning minimal latent directed trees. We analyze the sample complexity of the learning task when the empirical estimator of mutual information is used as the discrepancy measure.
authors.affiliation: Department of Industrial and Enterprise Systems Engineering, Coordinated Science Laboratory, University of Illinois at Urbana Champaign, Urbana, IL 61801, U.S.A. etesami2@illinois.edu.
authors.forename: Jalal
authors.initials: J
authors.lastname: Etesami
authors.affiliation: Department of Industrial and Enterprise Systems Engineering, Coordinated Science Laboratory, and Department of Electrical and Computer Engineering, University of Illinois at Urbana Champaign, Urbana, IL 61801, U.S.A. kiyavash@illinois.edu.
authors.forename: Negar
authors.initials: N
authors.lastname: Kiyavash
authors.affiliation: Department of Bioengineering, University of California, San Diego, La Jolla, CA 92093, U.S.A. tpcoleman@ucsd.edu.
authors.forename: Todd
authors.initials: T
authors.lastname: Coleman