Search papers, labs, and topics across Lattice.
This paper introduces a novel embedding technique for irregular time series data within Log-NCDEs, avoiding explicit reconstruction of continuous observation paths. They prove that compact-set universality transfers from the model input space to the data space under continuous and injective embeddings, justifying their approach. Their method, which records observations as increments and composes them into log-signatures, demonstrates accuracy, efficiency, and robustness on synthetic and real-world time-series datasets.
Forget interpolating: Log-NCDEs can directly process irregular time series by embedding observations as increments and composing them into log-signatures, bypassing the need for explicit reconstruction.
Continuous-time models are a natural choice for irregular and asynchronous data. A central design choice is how to embed discrete observations into continuous time. Interpolation- and imputation-based embeddings reconstruct a continuous observation path, making the model sensitive to the choice of reconstruction. We show that this reconstruction step is unnecessary; under mild conditions, compact-set universality on the model input space transfers to the data space whenever the embedding from data to input is continuous and injective. Guided by this result, and building on the rectilinear control path for Neural Controlled Differential Equations (NCDEs), we introduce a continuous and injective embedding for Log-NCDEs, a universal class of continuous-time models. Our approach records observations as increments and composes them over arbitrary query intervals to directly form log-signatures. This provides interval-level summaries without first interpolating the observed variables, while supporting online computation. Experiments on synthetic controlled dynamics and real-world time-series datasets show that the representation is accurate, efficient, and robust to irregular, asynchronous, and sparse observations.
