Structured Black Box Variational Inference for Latent Time Series Models
This work addresses a computational bottleneck for researchers and practitioners using Bayesian non-conjugate latent time series models, offering an incremental improvement in efficiency.
The authors tackled the problem of scaling black box variational inference for structured latent time series models, which typically scales quadratically with time steps, by developing an algorithm analogous to forward-backward that scales linearly, enabling efficient training of models like dynamic word embeddings.
Continuous latent time series models are prevalent in Bayesian modeling; examples include the Kalman filter, dynamic collaborative filtering, or dynamic topic models. These models often benefit from structured, non mean field variational approximations that capture correlations between time steps. Black box variational inference with reparameterization gradients (BBVI) allows us to explore a rich new class of Bayesian non-conjugate latent time series models; however, a naive application of BBVI to such structured variational models would scale quadratically in the number of time steps. We describe a BBVI algorithm analogous to the forward-backward algorithm which instead scales linearly in time. It allows us to efficiently sample from the variational distribution and estimate the gradients of the ELBO. Finally, we show results on the recently proposed dynamic word embedding model, which was trained using our method.