Conditional probability table

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In statistics, the conditional probability table (CPT) is defined for a set of discrete (not independent) random variables to demonstrate marginal probability of a single variable with respect to the others. For example, assume there are three random variables x_1,x_2, x_3 where each have K states. Then, the conditional probability table of x_1 provides the marginal probability values for P(x_1\mid x_2,x_3). Clearly, this table has K3 cells. In general, for M number of variables x_1,x_2,\ldots,x_M with K states, the CPT has size KM.[1]

CPT table can be put into a matrix form. For example, the values of P(x_j\mid x_i)=T_{ij} create a matrix. This matrix is a stochastic matrix since sum of all its elements is equals to 1; i.e. \sum_j T_{ij}.


  1. ^ Murphy, KP (2012). Machine learning: a probabilistic perspective. The MIT Press.