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## Part II

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**Part II**White Parts from: Technical overview for machine-learning researcher – slides from UAI 1999 tutorial**= Ct,h**Example: for (ht + htthh), we get p(d|m) = 3!2!/6!**Numerical example for the network X1 X2**Imaginary sample sizes denoted N’ijk Data: (true, true) and (true, false)**Used so far**Desired**How do we assign structure and parameter priors ?**Structure priors: Uniform, partial order (allowed/prohibited edges), proportional to similarityto some a priori network.**BDe**K2**So how to generate parameter priors?**Example: Suppose the hyper distribution for (X1,X2) is Dir( a00, a01 ,a10, a11).**Example: Suppose the hyper distribution for (X1,X2) is Dir(**a00, a01 ,a10, a11) This determines a Dirichlet distribution for the parameters of both directed models.**Summary: Suppose the parameters for (X1,X2) are distributed**Dir( a00, a01 ,a10, a11). Then, parameters for X1 are distributed Dir(a00+a01 ,a10+a11). Similarly, parameters for X2 are distributed Dir(a00+a10 ,a01+a11).**Functional Equations Example**• Example: f(x+y) = f(x) f(y) • Solution: (ln f )`(x+y) = (ln f )`(x) • and so: (ln f )`(x) = constant • Hence: (ln f )(x) = linear function • hence: f(x) = c eax • Assumptions: Positive everywhere, Differentiable