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Propagating distributions up directed acyclic graphs

E B Baum1, W D Smith

  • 1NEC Research Institute, 4 Independence Way, Princeton NJ 08540, USA. eric@research.nj.nec.com

Neural Computation
|February 9, 1999
PubMed
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This study extends game tree analysis to directed acyclic graphs (DAGs), addressing correlations in probability distributions. An exact algorithm for propagating distributions in game DAGs is presented, proving #P completeness and suggesting heuristic approaches.

Area of Science:

  • Artificial Intelligence
  • Game Theory
  • Computational Complexity

Background:

  • Previous work modeled game trees as graphical models with probabilistic evaluation functions.
  • Game positions can repeat, collapsing trees into directed acyclic graphs (DAGs), inducing dependencies.
  • Existing algorithms for game trees do not directly handle the correlations present in DAG structures.

Purpose of the Study:

  • To extend probabilistic game tree algorithms to handle directed acyclic graphs (DAGs).
  • To develop and analyze an algorithm for propagating probability distributions in game DAGs.
  • To investigate the computational complexity of distribution propagation in game DAGs.

Main Methods:

  • Developed an algorithm for propagating probability distributions up a game DAG, accounting for induced dependencies.

Related Experiment Videos

  • Analyzed the worst-case time complexity of the exact propagation algorithm.
  • Proved the #P completeness of correctly propagating distributions in game DAGs.

    • Main Results:

    • An algorithm for exact distribution propagation in game DAGs was successfully formulated.
    • The problem of correctly propagating distributions in game DAGs was proven to be #P complete.
    • The exact algorithm's exponential worst-case complexity was established.

    Conclusions:

    • Extending game tree analysis to DAGs requires addressing inter-node dependencies.
    • Exact distribution propagation in game DAGs is computationally intractable (#P complete).
    • A fast, inexact heuristic can be derived from the exact propagation algorithm for practical applications.