Faithful Embeddings of Irregular and Asynchronous Data for Online Log-NCDEs

2026-05-28

AI Summary

This work addresses the challenge of modeling irregularly and asynchronously observed time series data by proposing a continuous-time embedding method that operates without interpolation or imputation. The approach directly encodes observations as increments and constructs a continuous, injective embedding via the log-signature over intervals, enabling online computation while avoiding full path reconstruction. Built upon the Log-NCDE framework and the concept of rectangular control paths, the proposed embedding preserves the structural fidelity of the original data and maintains universality over compact subsets of the input space. Empirical evaluations demonstrate that the method achieves high accuracy, computational efficiency, and strong robustness to sparsity and asynchronicity across both synthetic dynamical systems and real-world temporal datasets.

Abstract

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.

Problem

• irregular data
• asynchronous data
• continuous-time models
• faithful embeddings
• online computation

Innovation

• Log-NCDE
• continuous-time embedding
• injective embedding
• log-signature
• irregular time series