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Independence of Causal Influence

This paper explores the representation of probabilistic graphical models with an emphasis on local structure and independence of causal influence within the context of various respiratory illnesses, including pneumonia, flu, tuberculosis, and bronchitis. We delve into the behavioral aspects of conditional probability distributions (CPD) and sigmoid functions as they relate to these conditions. Our analysis is supported by extensive empirical data, estimating the number of parameters required for effective modeling, thus enhancing our understanding of the probabilistic relationships involved in these diseases.

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Independence of Causal Influence

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  1. Representation Probabilistic Graphical Models Local Structure Independence of Causal Influence

  2. . . . Pneu- monia Flu TB Bron- chitis Cough

  3. Noisy OR CPD X1 X2 Xk . . . Z0 Z1 Z2 Zk P(Z0=1) =0 Xi=0 P(Zi=1|Xi) = Y Xi=1

  4. Independence of Causal Influence X1 X2 Xk . . . Z0 Z1 Z2 Zk Z Y

  5. Sigmoid CPD X1 X2 Xk . . . Z1 Z2 Zk Z Y

  6. Behavior of Sigmoid CPD w0 = -5 multiply w and w0 by 10

  7. CPCS M. Pradhan G. Provan B. Middleton M. Henrion UAI 1994 # of parameters: 133,931,430 to 8254

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