Learnable Path in Neural Controlled Differential Equations

About

Neural controlled differential equations (NCDEs), which are continuous analogues to recurrent neural networks (RNNs), are a specialized model in (irregular) time-series processing. In comparison with similar models, e.g., neural ordinary differential equations (NODEs), the key distinctive characteristics of NCDEs are i) the adoption of the continuous path created by an interpolation algorithm from each raw discrete time-series sample and ii) the adoption of the Riemann--Stieltjes integral. It is the continuous path which makes NCDEs be analogues to continuous RNNs. However, NCDEs use existing interpolation algorithms to create the path, which is unclear whether they can create an optimal path. To this end, we present a method to generate another latent path (rather than relying on existing interpolation algorithms), which is identical to learning an appropriate interpolation method. We design an encoder-decoder module based on NCDEs and NODEs, and a special training method for it. Our method shows the best performance in both time-series classification and forecasting.

Sheo Yon Jhin, Minju Jo, Seungji Kook, Noseong Park, Sungpil Woo, Sunhwan Lim · 2023

Related benchmarks

Task	Dataset	Result
Audio Classification	Speech Commands (test)	Accuracy92.2	65
Multivariate Time Series Classification	UEA 30% missing rate (test)	Accuracy45.9	39
Classification	BasicMotions 50% Missing	Accuracy31.7	38
Time-series classification	18 UEA datasets Regular	Accuracy49	38
Time-series classification	UEA 18 datasets 70% Missing	Accuracy45.1	34
Forecasting	MuJoCo Regular (test)	MSE0.022	27
Forecasting	MuJoCo 30% Dropped (test)	MSE0.022	27
Forecasting	MuJoCo 50% Dropped (test)	MSE0.022	27
Forecasting	MuJoCo 70% Dropped (test)	MSE0.022	27
Time-series classification	30 benchmark datasets Regular (test)	Accuracy44.4	25