How can Dirichlet smoothing be used as an IDF component to estimate the probabilities of a Topic model ? i.e, Smoothing with a background collection model to estimate topic model ?
I've seen many articles suggesting that Smoothing serves two purposes :
To avoid the zero-probability scenario for words
To act as a discriminative component (IDF) along with a collection model to avoid giving higher probabilities to common words like , 'the' , 'a' etc while estimating a topic model
What I don't understand is , how can Dirichlet smoothing , as shown below ( Estimation of word in a topic model )
I've worked out some examples but I don't get lesser probabilities for such common words . In fact , we are only adding pseudo counts to every word. So , how is IDF done using Dirichlet ?
I'm finding it hard to understand this . Please explain in detail .
Thanks in advance !