Long-term Forecasting using Higher Order Tensor RNNs

TL;DR

This paper introduces HOT-RNN, a novel neural architecture leveraging higher-order moments and tensor decompositions to improve long-term multivariate forecasting in nonlinear dynamic systems.

Contribution

The paper proposes HOT-RNN, a new recurrent neural network architecture that models nonlinear dynamics using higher-order tensors and tensor-train decomposition, with theoretical guarantees and improved long-term forecasting performance.

Findings

Achieves 5-12% better long-term prediction accuracy than RNNs and LSTMs.

Provides theoretical approximation guarantees and variance bounds for HOT-RNN.

Demonstrates effectiveness on simulated and real-world nonlinear time series data.

Abstract

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.