Latent ODEs for Irregularly-Sampled Time Series

8 Jul 2019  ·  Yulia Rubanova, Ricky T. Q. Chen, David Duvenaud ·

Time series with non-uniform intervals occur in many applications, and are difficult to model using standard recurrent neural networks (RNNs). We generalize RNNs to have continuous-time hidden dynamics defined by ordinary differential equations (ODEs), a model we call ODE-RNNs. Furthermore, we use ODE-RNNs to replace the recognition network of the recently-proposed Latent ODE model. Both ODE-RNNs and Latent ODEs can naturally handle arbitrary time gaps between observations, and can explicitly model the probability of observation times using Poisson processes. We show experimentally that these ODE-based models outperform their RNN-based counterparts on irregularly-sampled data.

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Results from the Paper


Task Dataset Model Metric Name Metric Value Global Rank Result Benchmark
Multivariate Time Series Imputation MuJoCo Latent ODE (ODE enc) MSE (10^2, 50% missing) 0.285 # 1
Multivariate Time Series Forecasting MuJoCo Latent ODE (ODE enc) MSE (10^-2, 50% missing) 1.258 # 1
Multivariate Time Series Forecasting MuJoCo ODE-RNN MSE (10^-2, 50% missing) 26.463 # 5
Multivariate Time Series Imputation MuJoCo ODE-RNN MSE (10^2, 50% missing) 0.665 # 3
Time Series Classification PhysioNet Challenge 2012 Latent ODE + Poisson AUC 82.6% # 12
AUC Stdev 0.7% # 4
Multivariate Time Series Imputation PhysioNet Challenge 2012 Latent ODE + Poisson mse (10^-3) 2.789 # 2
Multivariate Time Series Forecasting PhysioNet Challenge 2012 Latent ODE (ODE enc) mse (10^-3) 2.231 # 2
MSE stdev 0.029 # 1
Time Series Classification PhysioNet Challenge 2012 ODE-RNN AUC 83.3% # 10
AUC Stdev 0.9% # 3
Multivariate Time Series Forecasting PhysioNet Challenge 2012 Latent ODE + Poisson mse (10^-3) 2.208 # 1
MSE stdev 0.050 # 2
Time Series Classification PhysioNet Challenge 2012 Latent ODE (ODE enc AUC 82.9% # 11
AUC Stdev 0.4% # 6
Multivariate Time Series Imputation PhysioNet Challenge 2012 Latent ODE (ODE enc) mse (10^-3) 2.118 # 1

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