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Applications of PGMs and relation and conversion of Bayes and Markov's model

In this article, we will know more about PGMs: its application, Relation between Bayes network and Markov's Random field and conversion of Bayes network into Markov's random field.
Submitted by Bharti Parmar, on March 16, 2019

Application of PGMs: (Use cases)

  • Netflix, Amazon, facebook all use PGM recommend what is best for you.
  • This algorithm, Use the latent factor model and non-negative matrix factorization.
  • In politics American presidential polls using PGMs for prediction. FiveThirtyEight company that makes a prediction about American presidential polls using PGMs.
  • PGM is also inferred whether one is a MODI and KEJRIWAL supporter.

How Bayes network and Markov Random Fields Model related to each other:

PGMs diagram 1 For P(A, B) = P(A) * P(B/A) For P(A,B) α Ф(A,B)
PGMs diagram 2 For chain: P(A,B) = P(A) P(B/A) P(C/B) For chain: P(A,B) α Ф(A,B) Ф(B,C)
PGMs diagram 3 Shared parents: P(A,B,C) = P(A) P(B/A) P(C/B) Shared parents: P(A,B,C) α Ф(A,B) Ф(A,C)
Ф(A,B) ← P(A) P(B\A)
Ф(A,C) ← P(C\A)
PGMs diagram 4 Two parent shared a child: P(A,B,C) = P(A) P(B) P(C\A,B) A and B are independent given C P(A,B,C) α Ф(A,C) Ф(B,C)

Converting Bayes network into Markov random fields:

PGMs diagram 5

Moralizing parents: P (A, B, C) α Ф(A,C) Ф(B,C) where A and B are independent given C

  • Moralize all co-parents
  • More challenging is that Lose marginal independence of parents.
    PGMs diagram 6

Basically, it given an interference class of all directed graphical models and a class of all undirected graphical model are different but overlap each other.

Conclusion: In this article we have learnt about application of PGMs, how bayes network is related to markov's random field and conversion of bayes network into Markov's network model.


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