# Efficient Learning of Mixed Membership Models

## TL;DR

This paper introduces an efficient algorithm for learning mixed membership models that significantly reduces computational complexity and addresses issues with empirical estimators, demonstrating competitive results on various datasets.

## Contribution

The paper proposes a novel, scalable algorithm for mixed membership models that improves over tensor methods and provides theoretical guarantees.

## Key findings

- Reduces tensor decomposition complexity from O(p^3) to factorizing O(p/k) sub-tensors.
- Addresses negative entries in empirical moment estimators with provable conditions.
- Achieves competitive results on simulated and real datasets.

## Abstract

We present an efficient algorithm for learning mixed membership models when the number of variables $p$ is much larger than the number of hidden components $k$. This algorithm reduces the computational complexity of state-of-the-art tensor methods, which require decomposing an $O\left(p^3\right)$ tensor, to factorizing $O\left(p/k\right)$ sub-tensors each of size $O\left(k^3\right)$. In addition, we address the issue of negative entries in the empirical method of moments based estimators. We provide sufficient conditions under which our approach has provable guarantees. Our approach obtains competitive empirical results on both simulated and real data.