Learnable Path in Neural Controlled Differential Equations
This work addresses a specific bottleneck in NCDEs for researchers in time-series analysis, offering an incremental improvement over existing interpolation methods.
The authors tackled the problem of suboptimal path creation in Neural Controlled Differential Equations (NCDEs) for time-series processing by introducing a learnable latent path method, which achieved state-of-the-art performance in classification and forecasting tasks.
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.