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The Theoretical and Practical Beauty of Acyclic Directed Probabilistic Graphical Models
Marek J. Druzdzel
School of Information Sciences, University of Pittsburgh
Pittsburgh, PA, USA, [email protected]
Faculty of Computer Science, Bialystok University of Technology
Bialystok, Poland, [email protected]
In this talk, I will provide an overview of the last three decades of research on acyclic directed
probabilistic graphical models, also known as DAGs in the statistical community or Bayesian networks
in computer science and artificial intelligence. Mathematically, they offer an efficient representation
of joint probability distributions through factorization and subsequent explicit representation of
conditional independences. In practice, they are an intuitive and convenient to use modeling
formalism for problems that involve uncertainty. There exist efficient algorithms for deriving
posterior probability distributions over variables of interest given observation of other variables in
the network. Directed probabilistic graphs have been also extended to time-dependent domains and
are capable of modeling dynamical systems. They can be built based on expert knowledge but also
learned from data. Acyclic directed graphs are a convenient tool for modeling causality and
theoretical links have been proposed between probability and causation, leading to powerful
methods for discovery of causal relationships from data.
Bayesian network’s ability to model uncertain relations in an intuitive and compact way, along with
the existence of efficient algorithms for reasoning about these relations, have led to their enormous
popularity and an explosion of their applications in both academia and industry. I will introduce
Bayesian networks, provide a brief overview of the state of the art in directed probabilistic graphical
models, and show the relationship between directed probabilistic graphs and models based on
systems of simultaneous equations. While there is a sound theory underlying all this work, my
primary focus will be intuition.