Inferring from a model is the same as finding the conditional probability distribution over some variables, that is, , where and . Also, if we think about predicting values for a new data point, we are basically trying to find the conditional probability of the unknown variable, given the observed values of other variables. These conditional distributions can easily be computed from the joint probability distribution of the variables, by marginalizing and reducing them over variables and states.

Fig 3.1: The restaurant model

Let's consider the restaurant example once again, as shown in the preceding figure. We can think of various inference queries that we can try on the model. For example, we may want to find the probability of the quality of a restaurant being good, given that the location is good, the cost is high, and the number of people coming is also high, which would result in the probability query . Also, if we think of a machine learning problem, where we want to predict...