For categorical and multinomial distributions, the fitted values are an ( " M " + 1 )-vector of probabilities, with the property that all probabilities add up to 1.
42.
Considering observations in the form of co-occurrences ( w, d ) of words and documents, PLSA models the probability of each co-occurrence as a mixture of conditionally independent multinomial distributions:
43.
Named joint distributions that arise frequently in statistics include the multivariate normal distribution, the multivariate stable distribution, the multinomial distribution, the negative multinomial distribution, the multivariate hypergeometric distribution, and the elliptical distribution.
44.
Named joint distributions that arise frequently in statistics include the multivariate normal distribution, the multivariate stable distribution, the multinomial distribution, the negative multinomial distribution, the multivariate hypergeometric distribution, and the elliptical distribution.
45.
For the multinomial distribution, and for the vector form of the categorical distribution, the expected values of the elements of the vector can be related to the predicted probabilities similarly to the binomial and Bernoulli distributions.
46.
Note that, in some fields, such as natural language processing, the categorical and multinomial distributions are conflated, and it is common to speak of a " multinomial distribution " when a categorical distribution is actually meant.
47.
Note that, in some fields, such as natural language processing, the categorical and multinomial distributions are conflated, and it is common to speak of a " multinomial distribution " when a categorical distribution is actually meant.
48.
In this case, the joint distribution needs to be taken over all words in all documents containing a label assignment equal to the value of z _ d, and has the value of a Dirichlet-multinomial distribution.
49.
Although it is in fact possible to rewrite it as a product of such individual sums, the number of factors is very large, and is not clearly more efficient than directly computing the Dirichlet-multinomial distribution probability.
50.
In networks that include categorical variables with marginalized out ) of the network, which introduces dependencies among the various categorical nodes dependent on a given prior ( specifically, their joint distribution is a Dirichlet-multinomial distribution ).
