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The legend is wrong (or very misleading), while the code snippet displays the correct output. In the third example, given $E$, the highlighted node in grey, $A$ and $S$ are not d-separated. In this elementary configuration, $E$ is called a collider, and in a collider, conditioning on the common effect $E$ makes $A$ and $S$ dependent on each other. See for ...


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That is just a function of the question being asked here. You want to know if you can say Travel is dependent on Education to a degree not explained by the Occupation and Residence factors. You're not asking what Education is dependent on, nor are you asking whether Age and Sex are or are not a factors in Travel. You either know or assume the conditional ...


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I would do it like this: \begin{align} P(A,D|C) &= P(A|D,C)P(D|C)\\ &=\frac{P(D,C|A)P(A)}{P(D,C)}P(D|C)\\ &=\frac{P(D|C,A)P(C|A)P(A)}{P(D|C)P(C)}P(D|C)\\ &=\frac{P(C|A)P(A)}{P(C)}P(D|C)\\ &=P(A|C)P(D|C) \end{align} Where passages are just Bayes theorem and axioms of probability. I also used that $P(D|C,A) = P(D|C)$ because of redundancy ...


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Based on those definitions: Nonparametric:Algorithms that do not make strong assumptions about the form of the mapping function are called nonparametric machine learning algorithms. By not making assumptions, they are free to learn any functional form from the training data. EX: k-Nearest Neighbors, Decision Trees Parametric:Assumptions can greatly ...


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You're correct, when one is given the other can be inferred. This is always the case if the variables are dependent. But, the discussion in the text is about causality. Bayesian networks encode causal relationships. So, the direction of the arrows is the flow of causality in the model. Otherwise, you'd have always arrows in both directions. The word ...


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