论文标题
神经跳跃普通微分方程：一致的连续时间预测和过滤
Neural Jump Ordinary Differential Equations: Consistent Continuous-Time Prediction and Filtering
论文作者
论文摘要
神经ODE与复发性神经网络（RNN）（如Gru-ode-bayes或Ode-RNN）的组合非常适合模拟不规则观察到的时间序列。尽管这些模型的表现优于现有的离散时间方法，但没有理论保证其预测能力。假设不规则采样的时间序列数据源自连续的随机过程，则$ l^2 $ - 最佳的在线预测是当前可用信息的有条件期望。我们介绍了神经跳跃颂歌（NJ-ODE），该神经跳跃（NJ-ODE）提供了一种数据驱动的方法，可以不断地学习随机过程的有条件期望。我们的方法模拟了两种神经颂观察之间的条件期望，每当进行新的观察结果时跳跃。我们定义了一个新颖的培训框架，这使我们能够首次证明理论保证。特别是，我们表明我们的模型输出收敛到$ l^2 $ - 最佳预测。这可以解释为解决特殊过滤问题的解决方案。我们提供的实验表明，理论结果也从经验上持有。此外，我们在实验上表明，我们的模型在更复杂的学习任务中优于基准，并在现实世界数据集上进行比较。
Combinations of neural ODEs with recurrent neural networks (RNN), like GRU-ODE-Bayes or ODE-RNN are well suited to model irregularly observed time series. While those models outperform existing discrete-time approaches, no theoretical guarantees for their predictive capabilities are available. Assuming that the irregularly-sampled time series data originates from a continuous stochastic process, the $L^2$-optimal online prediction is the conditional expectation given the currently available information. We introduce the Neural Jump ODE (NJ-ODE) that provides a data-driven approach to learn, continuously in time, the conditional expectation of a stochastic process. Our approach models the conditional expectation between two observations with a neural ODE and jumps whenever a new observation is made. We define a novel training framework, which allows us to prove theoretical guarantees for the first time. In particular, we show that the output of our model converges to the $L^2$-optimal prediction. This can be interpreted as solution to a special filtering problem. We provide experiments showing that the theoretical results also hold empirically. Moreover, we experimentally show that our model outperforms the baselines in more complex learning tasks and give comparisons on real-world datasets.
