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Yulia Rubanova; Ricky T. Q. Chen; David Duvenaud
Abstract
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.
Code Repositories
Benchmarks
| Benchmark | Methodology | Metrics |
|---|---|---|
| multivariate-time-series-forecasting-on-1 | ODE-RNN | MSE (10^-2, 50% missing): 26.463 |
| multivariate-time-series-forecasting-on-1 | Latent ODE (ODE enc) | MSE (10^-2, 50% missing): 1.258 |
| multivariate-time-series-forecasting-on-2 | Latent ODE (ODE enc) | MSE stdev: 0.029 mse (10^-3): 2.231 |
| multivariate-time-series-forecasting-on-2 | Latent ODE + Poisson | MSE stdev: 0.05 mse (10^-3): 2.208 |
| multivariate-time-series-imputation-on-1 | Latent ODE (ODE enc) | mse (10^-3): 2.118 |
| multivariate-time-series-imputation-on-1 | Latent ODE + Poisson | mse (10^-3): 2.789 |
| multivariate-time-series-imputation-on-mujoco | ODE-RNN | MSE (10^2, 50% missing): 0.665 |
| multivariate-time-series-imputation-on-mujoco | Latent ODE (ODE enc) | MSE (10^2, 50% missing): 0.285 |
| time-series-classification-on-physionet | ODE-RNN | AUC: 83.3% AUC Stdev: 0.9% |
| time-series-classification-on-physionet | Latent ODE + Poisson | AUC: 82.6% AUC Stdev: 0.7% |
| time-series-classification-on-physionet | Latent ODE (ODE enc | AUC: 82.9% AUC Stdev: 0.4% |
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