Latent Dirichlet Allocation

3.2 A continuous mixture of unigrams

1. How can LDA be seen as a continuous mixture of unigrams?
   Marginalizing out \(z\) gives a word distribution \(p(w \mid \theta, \beta) = \sum_z p(w \mid z, \beta)\, p(z \mid \theta)\) that depends on the random \(\theta\). So \(p(\mathbf{w} \mid \alpha, \beta) = \int p(\theta \mid \alpha) \prod_n p(w_n \mid \theta, \beta)\, d\theta\): a continuous mixture of unigram models with mixture weights \(p(\theta \mid \alpha)\), using only \(k + kV\) parameters.
   • Blei et al., 2003, Latent Dirichlet Allocation (Journal of Machine Learning Research), §3.2, pp. 998–999