Conditional probability table: Difference between revisions

Revision as of 20:12, 23 December 2013

Revision as of 20:13, 23 December 2013

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In [[statistics]], the Conditional Probability Table (CPT) is defined for a set of discrete (not independent) [[random variable]] to demonstrate [[marginal probability]] of a single variable with respect to the others. For example, assume there are three random variables <math>x_1,x_2, x_3</math> where each have <math>K</math> states. Then, the conditional probability table of <math>x_1</math> provides the marginal probability math values for <math>P(x_1|x_2,x_3)</math>. Clearly, this table has <math>O(K^3)</math> number of rows. In general, for <math>M</math> number of variables <math>x_1,x_2,...,x_M</math> with <math>K</math> states, the CPT has the size of <math>O(K^M)</math>.

CPT table can be put into a matrix form. For example, the values of <math>P(x_j|x_i)=T_{ij}</math> create a matrix. This matrix is [[Stochastic matrix]] since its row sum is equals to 1; i.e. <math>\sum_j T_ijT_{ij}</math>.

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