Conditional probability table: Difference between revisions

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In [[statistics]], the '''conditional probability table (CPT)''' is defined for a set of discrete and mutually [[independence (probability)|dependent]] [[random variable]]s to demonstrate [[conditional 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 conditional probability values for <math>P(x_1\mid x_2,x_3)</math>. This table has <math>K^3</math> cells. In general, for <math>M</math> variables <math>x_1,x_2,\ldots,x_M</math> with <math>K</math> states, the CPT has size&nbsp;<math>K^M.</math><ref name=murphybook>{{cite book|last=Murphy|first=KP|title=Machine learning: a probabilistic perspective|year=2012|publisher=The MIT Press}}</ref>

AWith only two variables, a CPT can be put into a matrix form. For example, the values of <math>P(x_j\mid x_i)=T_{ij}</math> create a matrix. This matrix is a [[stochastic matrix]] since the rows sum to 1; i.e. <math>\sum_j T_{ij} = 1</math> for all ''i''.

==References==