Guaranteed inference in topic models
This addresses the need for reliable inference in topic models, especially for data streams, offering a solution with provable guarantees where previous methods were approximate and lacked such assurances.
The paper tackles the problem of posterior inference in topic models, which is often intractable, by introducing the Online Maximum a Posteriori Estimation (OPE) algorithm that provides theoretical guarantees on quality and fast convergence rates.
One of the core problems in statistical models is the estimation of a posterior distribution. For topic models, the problem of posterior inference for individual texts is particularly important, especially when dealing with data streams, but is often intractable in the worst case. As a consequence, existing methods for posterior inference are approximate and do not have any guarantee on neither quality nor convergence rate. In this paper, we introduce a provably fast algorithm, namely Online Maximum a Posteriori Estimation (OPE), for posterior inference in topic models. OPE has more attractive properties than existing inference approaches, including theoretical guarantees on quality and fast rate of convergence to a local maximal/stationary point of the inference problem. The discussions about OPE are very general and hence can be easily employed in a wide range of contexts. Finally, we employ OPE to design three methods for learning Latent Dirichlet Allocation from text streams or large corpora. Extensive experiments demonstrate some superior behaviors of OPE and of our new learning methods.