Virtually all methods of learning dynamic systems from data startwith the same basic assumption: the learning algorithm will be given atime sequence of data generated from the dynamic system. We considerthe case where the training data comes from the system's operation butwith no temporal ordering. The data are simply drawn as individualdisconnected points. While making this assumption may seem absurd atfirst glance, we observe that many scientific modeling tasks haveexactly this property.
We propose several methods for solving this problem. We write down anapproximate likelihood function that may be optimized to learn dynamicmodels and show how kernel methods can be used to obtain non-linearmodels. We propose an alternative method that focuses on achievingtemporal smoothness in the learned dynamics. Finally, we consider thecase where a small amount of sequenced data is available along with alarge amount of non-sequenced data. We propose the use of the Lyapunovequation and the non-sequenced data to provide regularization whenperforming regression on the sequenced data to learn a dynamic model.We demonstrate our methods on synthetic data and describe the resultsof our analysis of some bioinformatics data sets.