  Probabilistic forecasting of high dimensional multivariate time series is a
notoriously challenging task, both in terms of computational burden and
distribution modeling. Most previous work either makes simple distribution
assumptions or abandons modeling cross-series correlations. A promising line of
work exploits scalable matrix factorization for latent-space forecasting, but
is limited to linear embeddings, unable to model distributions, and not
trainable end-to-end when using deep learning forecasting. We introduce a novel
temporal latent auto-encoder method which enables nonlinear factorization of
multivariate time series, learned end-to-end with a temporal deep learning
latent space forecast model. By imposing a probabilistic latent space model,
complex distributions of the input series are modeled via the decoder.
Extensive experiments demonstrate that our model achieves state-of-the-art
performance on many popular multivariate datasets, with gains sometimes as high
as $50\%$ for several standard metrics.
