Learning Interpretable Deep State Space Model for
Probabilistic Time Series Forecasting
Abstract
Probabilistic time series forecasting involves estimating the distribution of future based on its history, which is essential for risk management in
downstream decision-making. We propose a deep
state space model for probabilistic time series forecasting whereby the non-linear emission model and
transition model are parameterized by networks
and the dependency is modeled by recurrent neural
nets. We take the automatic relevance determination (ARD) view and devise a network to exploit
the exogenous variables in addition to time series.
In particular, our ARD network can incorporate the
uncertainty of the exogenous variables and eventually helps identify useful exogenous variables and
suppress those irrelevant for forecasting. The distribution of multi-step ahead forecasts are approximated by Monte Carlo simulation. We show in
experiments that our model produces accurate and
sharp probabilistic forecasts. The estimated uncertainty of our forecasting also realistically increases
over time, in a spontaneous manner