Probabilistic Graphical Model Family

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A Probabilistic Graphical Model Family is a statistical model family that uses a graph structure to represent probability distributions between random variables.



References

2014


  • http://en.wikipedia.org/wiki/Graphical_model#Types_of_graphical_models
    • Generally, probabilistic graphical models use a graph-based representation as the foundation for encoding a complete distribution over a multi-dimensional space and a graph that is a compact or factorized representation of a set of independences that hold in the specific distribution. Two branches of graphical representations of distributions are commonly used, namely, Bayesian networks and Markov networks. Both families encompass the properties of factorization and independences, but they differ in the set of independences they can encode and the factorization of the distribution that they induce


2008

2006

2001

  • F. V. Jensen. (2001). Bayesian Networks and Decision Graphs. Springer.
    • Introductory book.

2000

1999

1998

1997

  • (Jordan, 1997) ⇒ Michael I. Jordan. (1997). “An Introduction to Graphical Models." Tutorial at NIPS-1997.
    • Graphical models are a marriage between graph theory and probability theory
    • They clarify the relationship between neural networks and related network-based models such as HMMs, MRFs, and Kalman lters
    • Indeed, they can be used to give a fully probabilistic interpretation to many neural network architectures
    • Some advantages of the graphical model point of view
      • inference and learning are treated together
      • supervised and unsupervised learning are merged seamlessly
      • missing data handled nicely
      • a focus on conditional independence and computational issues
      • interpretability (if desired)
  • (Mitchell, 1997) ⇒ Tom M. Mitchell. (1997). “Machine Learning." McGraw-Hill.

1996

  • (Lauritzen, 1996) ⇒ S. Lauritzen. (1996). “Graphical Models.” Oxford.
    • mathematical exposition of the theory of graphical models.

1988