Continuous Latent Adversarial Autoencoder: A Time-Sensitive Method for Incomplete Time-Series Modeling

Abstract

Incomplete time-series modeling is an unavoidable topic in real-world time-series analysis because of the frequent occurrence of missing values in practical data. However, integrating data preprocessing and subsequent analysis within a model can amplify the errors from processed values. Moreover, most existing methods that directly model incomplete time series often fail to infer values at any desired time or support multistep prediction. To address these issues, this article introduces a novel generative model called the continuous latent adversarial autoencoder (CLAAE) for directly modeling incomplete time series. CLAAE can effectively impute missing data of any time point and support multistep prediction. Specifically, CLAAE devises a time-aware long short-term memory (LSTM) encoder to extract temporal and sequential characteristics. The decoder is built upon the augmented neural ordinary differential equation (ANODE), allowing it to infer the probability of missing data across an arbitrary continuous-time horizon. To guarantee the meaningfulness of samples generated from any region within the prior space, a fully connected neural network is utilized as a discriminator, encouraging the aggregated posterior learned by the encoder to be indistinguishable from a selected prior distribution. Extensive experimental results across simulations and real-world datasets demonstrate that CLAAE outperforms baseline methods, especially when the amount of missing data is overwhelming. By combining the autoencoder and adversarial training, CLAAE can significantly enhance the quality of the synthetic samples, respecting the original feature distributions and the temporal dynamics.