Editing Generative model (section)

== Examples ==
=== Simple example ===
Suppose the input data is <math>x \in \{1, 2\}</math>, the set of labels for <math>x</math> is <math>y \in \{0, 1\}</math>, and there are the following 4 data points:
<math>(x,y) = \{(1,0), (1,1), (2,0), (2,1)\}</math>

For the above data, estimating the joint probability distribution <math>p(x,y)</math> from the [[empirical measure]] will be the following:
{| class="wikitable"
|-
!  !! <math>y=0
</math>!! <math>y=1
</math>
|-
| <math>x=1
</math> || <math>1/4
</math> ||<math>1/4
</math>
|-
| <math>x=2
</math> || <math>1/4
</math> || <math>1/4
</math>
|}

while <math>p(y|x)</math> will be following:
{| class="wikitable"
|-
!  !! <math>y=0
</math> !! <math>y=1
</math>
|-
| <math>x=1
</math>
| <math>1/2

</math> || <math>1/2
</math>
|-
| <math>x=2
</math> || <math>1/2
</math> || <math>1/2
</math>
|}

=== Text generation ===
{{harvtxt|Shannon|1948}} gives an example in which a table of frequencies of English word pairs is used to generate a sentence beginning with "representing and speedily is an good"; which is not proper English but which will increasingly approximate it as the table is moved from word pairs to word triplets etc.