Cubic Spline Smoothing Compensation for Irregularly Sampled Sequences

Jing Shi, Jing Bi, Yingru Liu, Chenliang Xu

Keywords: Neural Ordinary Differential Equations, Cubic Spline Interpolation, Irregular Time Series

Abstract:

The marriage of recurrent neural networks and neural ordinary differential networks (ODE-RNN) is effective in modeling irregularly sampled sequences.
While ODE produces the smooth hidden states between observation intervals, the RNN will trigger a hidden state jump when a new observation arrives and thus cause the interpolation discontinuity problem.
To address this issue, we propose the cubic spline smoothing compensation, which is a stand-alone module upon either the output or the hidden state of ODE-RNN and can be trained end-to-end.
We derive its analytical solution and provide its theoretical interpolation error bound.
Extensive experiments indicate its merits over both ODE-RNN and cubic spline interpolation.

One-sentence Summary: A cubic spline smoothing compensation to the ODE-RNN for irregular sampled sequence interpolation.

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