Long-term Forecasting using Higher Order Tensor RNNs
This work addresses the challenge of long-term forecasting in nonlinear dynamic systems for applications like time series analysis, though it appears incremental as it builds on existing RNN architectures with tensor methods.
The paper tackles long-term forecasting in nonlinear multivariate systems by introducing Higher-Order Tensor RNNs (HOT-RNNs), which learn nonlinear dynamics using higher-order moments and state transitions with tensor-train decomposition to reduce parameters, achieving 5% to 12% improvements over standard RNNs and LSTMs on simulated and real-world data.
We present Higher-Order Tensor RNN (HOT-RNN), a novel family of neural sequence architectures for multivariate forecasting in environments with nonlinear dynamics. Long-term forecasting in such systems is highly challenging, since there exist long-term temporal dependencies, higher-order correlations and sensitivity to error propagation. Our proposed recurrent architecture addresses these issues by learning the nonlinear dynamics directly using higher-order moments and higher-order state transition functions. Furthermore, we decompose the higher-order structure using the tensor-train decomposition to reduce the number of parameters while preserving the model performance. We theoretically establish the approximation guarantees and the variance bound for HOT-RNN for general sequence inputs. We also demonstrate 5% ~ 12% improvements for long-term prediction over general RNN and LSTM architectures on a range of simulated environments with nonlinear dynamics, as well on real-world time series data.