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GRU-ODE-Bayes: Continuous modeling of sporadically-observed time series (1905.12374v2)

Published 29 May 2019 in cs.LG and stat.ML

Abstract: Modeling real-world multidimensional time series can be particularly challenging when these are sporadically observed (i.e., sampling is irregular both in time and across dimensions)-such as in the case of clinical patient data. To address these challenges, we propose (1) a continuous-time version of the Gated Recurrent Unit, building upon the recent Neural Ordinary Differential Equations (Chen et al., 2018), and (2) a Bayesian update network that processes the sporadic observations. We bring these two ideas together in our GRU-ODE-Bayes method. We then demonstrate that the proposed method encodes a continuity prior for the latent process and that it can exactly represent the Fokker-Planck dynamics of complex processes driven by a multidimensional stochastic differential equation. Additionally, empirical evaluation shows that our method outperforms the state of the art on both synthetic data and real-world data with applications in healthcare and climate forecast. What is more, the continuity prior is shown to be well suited for low number of samples settings.

Citations (271)

Summary

  • The paper introduces GRU-ODE-Bayes, a novel model combining neural ODEs and Bayesian inference to continuously model sporadically observed multivariate time series data.
  • Empirical results show GRU-ODE-Bayes outperforms state-of-the-art methods, particularly on datasets with low sample sizes like healthcare (MIMIC-III) and climate data (USHCN).
  • This framework has significant implications for fields like healthcare and climate science, enabling improved analysis and prediction of irregular temporal data without requiring imputation.

Analyzing "GRU-ODE-Bayes: Continuous Modeling of Sporadically-Observed Time Series"

The paper "GRU-ODE-Bayes: Continuous Modeling of Sporadically-Observed Time Series" introduces a novel approach for handling sporadically observed, multivariate time series data through the GRU-ODE-Bayes model. This research builds upon existing frameworks in neural ordinary differential equations (ODEs) and Bayesian inference to improve the modeling of irregularly sampled time series data in domains such as healthcare and climate science.

Core Contributions

The authors propose a continuous-time recurrent neural network model that merges the capabilities of Gated Recurrent Units (GRUs) and neural ODEs, which they term GRU-ODE, with a Bayesian update mechanism. This integration allows the model to process sporadic observations directly and update its latent state representation. Moreover, this dual architecture is designed to estimate the probability distribution of future observations, addressing a critical need in forecasting applications.

Technical Insights and Comparisons

GRU-ODE-Bayes demonstrates several theoretical advancements. The GRU-ODE component operates on continuous time scales, thus naturally adhering to the intrinsic temporal continuity of the data, a stark contrast to traditional discrete approaches reliant on rigid time-stepping. Furthermore, the Bayesian update method (GRU-Bayes) efficiently incorporates new observations, updating the latent state with respect to incoming data while maintaining bounded hidden states, which is crucial for stability and interpretability.

The paper includes an empirical evaluation showing GRU-ODE-Bayes outperforms state-of-the-art methods, including regular GRUs with imputation strategies and NeuralODE-VAEs, particularly in cases presenting with low sample sizes. For instance, GRU-ODE-Bayes displayed strong performance on healthcare data from the MIMIC-III dataset and climatic data from USHCN, both marked by sparse temporal sampling. The methodology's ability to outperform encoders-decoder models such as NeuralODE-VAE is attributed to its ability to directly handle irregular data inputs, without the need for prior data imputation or binning, and to encode temporal dependencies efficiently even with few data points.

Implications and Future Directions

The theoretical robustness and empirical strengths of GRU-ODE-Bayes point to significant implications for fields dealing with irregularly sampled data. In healthcare, this method supports enhanced patient monitoring and prognosis by effectively modeling the temporal dynamics of sparse and irregular clinical data. Similarly, in climate science, it aids in the prediction and analysis of weather patterns where consistent data collection can be challenging due to environmental and logistical constraints.

Future work can extend GRU-ODE-Bayes to handle different types of data distributions, including categorical data, by extending Bayesian update capabilities beyond Gaussian observations. Additionally, exploring the use of GRU-ODE-Bayes in real-time applications could provide further insight into its robustness and adaptability in dynamic settings.

Conclusion

The GRU-ODE-Bayes framework stands as a substantial advance in continuous-time modelling of sporadically observed time series. Its ability to synthesize neural ODEs with Bayesian networks proposes a cohesive approach to handling real-world data's irregularities and inherently uncertain nature. With potential applications across numerous domains, GRU-ODE-Bayes exemplifies the power of integrating deterministic and probabilistic models in tackling complex temporal machine learning tasks.