Conditional Probability Models
Overview
Conditional Probability Models use
Bayes Rule
to represent a distribution as the result of multiplying various conditional probabilty factors.
In the most general form, the probability can be written as
{% p(x_1, ... , x_n) = \Pi_{n=1}^N p(x_n|x_1, ..., x_{n-1}) %}
Various models will simplify the above equation by layering additional assumptions onto it.
Independence
In the case of independence, each variable is assumed to be indepedent of the others. This results in
{% p(x_1, ... , x_n) = \Pi_{n=1}^N p(x_n) %}
Markov
{% p(x_1, ... , x_n) = p(x_1) \Pi_{n=2}^N p(x_n|x_{n-1}) %}
