Marginal and conditional probabilities

We can in turn define the marginal probabilities

$$p(x_i;\boldsymbol{\Theta}) = \frac{\sum_{h_j\in \boldsymbol{H}}f(x_i,h_j;\boldsymbol{\Theta})}{Z(\boldsymbol{\Theta})},$$

and

$$p(h_i;\boldsymbol{\Theta}) = \frac{\sum_{x_i\in \boldsymbol{X}}f(x_i,h_j;\boldsymbol{\Theta})}{Z(\boldsymbol{\Theta})}.$$

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