A fast algorithm with minimax optimal guarantees for topic models with an unknown number of topics

Understand

We propose a new method of estimation in topic models, that is not a variation on the existing simplex finding algorithms, and that estimates the number of topics K from the observed data.

• We derive new finite sample minimax lower bounds for the estimation of A, as well as new upper bounds for our proposed estimator.
• We describe the scenarios where our estimator is minimax adaptive.
• Our finite sample analysis is valid for any number of documents (n), individual document length (N_i), dictionary size (p) and number of topics (K), and both p and K are allowed to increase with n, a situation not handled well by previous analyses.