# P\'olya Urn Latent Dirichlet Allocation: a doubly sparse massively parallel sampler

## TL;DR

This paper introduces a novel, faster, and asymptotically exact parallel sampler for LDA that overcomes memory and convergence issues of previous methods, enabling efficient large-scale topic modeling.

## Contribution

A new Pólya-urn-based approximation for LDA sampling that is doubly sparse, parallelizable, and asymptotically exact, improving efficiency over existing methods.

## Key findings

- The proposed sampler is faster than previous Gibbs samplers.
- It is asymptotically exact as data size grows.
- Partially collapsed samplers can outperform fully collapsed ones.

## Abstract

Latent Dirichlet Allocation (LDA) is a topic model widely used in natural language processing and machine learning. Most approaches to training the model rely on iterative algorithms, which makes it difficult to run LDA on big corpora that are best analyzed in parallel and distributed computational environments. Indeed, current approaches to parallel inference either don't converge to the correct posterior or require storage of large dense matrices in memory. We present a novel sampler that overcomes both problems, and we show that this sampler is faster, both empirically and theoretically, than previous Gibbs samplers for LDA. We do so by employing a novel P\'olya-urn-based approximation in the sparse partially collapsed sampler for LDA. We prove that the approximation error vanishes with data size, making our algorithm asymptotically exact, a property of importance for large-scale topic models. In addition, we show, via an explicit example, that - contrary to popular belief in the topic modeling literature - partially collapsed samplers can be more efficient than fully collapsed samplers. We conclude by comparing the performance of our algorithm with that of other approaches on well-known corpora.