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''<sup>3</sup> 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 ''K''<sup>''M''</sup>.<ref name=murphybook>{{cite book|last=Murphy|first=KP|title=Machine learning: a probabilistic perspective|year=2012|publisher=The MIT Press}}</ref> |
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''<sup>3</sup> 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 ''K''<sup>''M''</sup>.<ref name=murphybook>{{cite book|last=Murphy|first=KP|title=Machine learning: a probabilistic perspective|year=2012|publisher=The MIT Press}}</ref> |
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Revision as of 02:26, 2 June 2014
 | This article needs additional citations for verification. (December 2013) |
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 where each have states. Then, the conditional probability table of provides the marginal probability values for . Clearly, this table has K3 cells. In general, for number of variables with states, the CPT has size KM.[1]
CPT table can be put into a matrix form. For example, the values of create a matrix. This matrix is stochastic matrix since its row sum is equals to 1; i.e. .
References
- ^ Murphy, KP (2012). Machine learning: a probabilistic perspective. The MIT Press.
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