Conditional probability table: Difference between revisions

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In [[statistics]], the '''conditional probability table (CPT)''' is defined for a set of discrete (not independent) [[random variable]]s 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 values for <math>P(x_1\mid x_2,x_3)</math>. Clearly, this table has ''K''³ cells. In general, for <math>M</math> number of variables <math>x_1,x_2,\ldots,x_M</math> with <math>K</math> states, the CPT has size&nbsp;''K''^''M''.<ref name=murphybook /><ref>{{cite book|last=Murphy|first=KP|title=Machine learning: a probabilistic perspective|year=2012|publisher=The MIT Press}}</ref>

CPT table 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 [[stochastic matrix]] since its row sum is equals to 1; i.e. <math>\sum_j T_{ij}</math>.

==References==

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<ref name=murphybook />

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[[Category:Probability theory]]