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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] and 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 networkâ€™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.