When to use Dirichlet distribution?

Dirichlet distributions are most commonly used as the prior distribution of categorical variables or multinomial variables in Bayesian mixture models and other hierarchical Bayesian models.

Is the Dirichlet distribution a conjugate prior for the categorical distribution?

In the scalar form, the Categorical distribution is a generalization of the Bernoulli dis- tribution (coin flipping). Dirichlet distribution as a prior. It turns out (to further the confusion), that the Dirich- let distribution is the conjugate prior for both the Categorical and Multinomial distributions!

How many parameters does a Dirichlet distribution take?

This diversity of shapes by varying only two parameters makes it particularly useful for modelling actual measurements. For the Dirichlet distribution Dir(α) we generalise these shapes to a K simplex.

What is Alpha in Dirichlet?

The dirichlet distribution has a single parameter, often referred to as the alpha parameter. This parameter determines both the distribution and concentration of the dirichlet. A higher alpha then gives a more dense distribution whereas a lower alpha gives a more sparse distribution.

What is a Dirichlet parameter?

The dirichlet distribution has a single parameter, often referred to as the alpha parameter. This parameter determines both the distribution and concentration of the dirichlet. In the example of a bag of dices, a dense distribution means that each die in the bag is likely to have a faily uniform PMF.

What is the formula for Dirichlet smoothing?

Dirichlet Smoothing: Pμ(w∣ˆθ)=c(w,D)+μP(w∣C)|D|+μ=|D||D|+μ⋅c(w,D)|D|+μμ+|D|⋅P(w∣C)

What is add K smoothing?

One alternative to add-one smoothing is to move a bit less of the probability mass from the seen to the unseen events. Instead of adding 1 to each count, we add a frac- tional count k (. This algorithm is therefore called add-k smoothing.