Neural Jump ODEs as Generative Models
This provides a method for generative modeling of stochastic processes without adversarial training, applicable to irregularly sampled and path-dependent data, which is incremental as it adapts existing NJODE frameworks to a new task.
The authors tackled the problem of generating samples from Itô processes by using Neural Jump ODEs (NJODEs) as generative models, proving that under standard assumptions, the learned coefficients recover the true parameters in the limit, enabling generation of samples with the same law as the underlying process.
In this work, we explore how Neural Jump ODEs (NJODEs) can be used as generative models for Itô processes. Given (discrete observations of) samples of a fixed underlying Itô process, the NJODE framework can be used to approximate the drift and diffusion coefficients of the process. Under standard regularity assumptions on the Itô processes, we prove that, in the limit, we recover the true parameters with our approximation. Hence, using these learned coefficients to sample from the corresponding Itô process generates, in the limit, samples with the same law as the true underlying process. Compared to other generative machine learning models, our approach has the advantage that it does not need adversarial training and can be trained solely as a predictive model on the observed samples without the need to generate any samples during training to empirically approximate the distribution. Moreover, the NJODE framework naturally deals with irregularly sampled data with missing values as well as with path-dependent dynamics, allowing to apply this approach in real-world settings. In particular, in the case of path-dependent coefficients of the Itô processes, the NJODE learns their optimal approximation given the past observations and therefore allows generating new paths conditionally on discrete, irregular, and incomplete past observations in an optimal way.