Extending Path-Dependent NJ-ODEs to Noisy Observations and a Dependent Observation Framework
The Path-Dependent Neural Jump Ordinary Differential Equation (PD-NJ-ODE) is a model for predicting continuous-time stochastic processes with irregular and incomplete observations. In particular, the method learns optimal forecasts given irregularly sampled time series of incomplete past observations. So far the process itself and the coordinate-wise observation times were assumed to be independent and observations were assumed to be noiseless. In this work we discuss two extensions to lift these restrictions and provide theoretical guarantees as well as empirical examples for them. In particular, we can lift the assumption of independence by extending the theory to much more realistic settings of conditional independence without any need to change the algorithm. Moreover, we introduce a new loss function, which allows us to deal with noisy observations and explain why the previously used loss function did not lead to a consistent estimator.
Code (1)
Tasks
Time SeriesSimilar Papers 제목 키워드 기반
Pathwise Learning of Stochastic Dynamical Systems with Partial Observations
The reconstruction and inference of stochastic dynamical systems from data is a fundamental task in inverse problems and statistical learning. While surrogate modeling advances computational methods to approximate these …
Learning to Assimilate in Chaotic Dynamical Systems
The accuracy of simulation-based forecasting in chaotic systems is heavily dependent on high-quality estimates of the system state at the time the forecast is initialized. Data assimilation methods are used to infer thes…
DenoisingExtracting Governing Equations from Latent Dynamics via Multi-View Contrastive Learning
Identifying latent dynamical systems from noisy, high-dimensional measurements is a central problem at the intersection of representation learning, system identification, and scientific discovery. We present DYSCO, a mul…
Representation LearningContrastive LearningGenerative Ensemble Regression: Learning Particle Dynamics from Observations of Ensembles with Physics-Informed Deep Generative Models
We propose a new method for inferring the governing stochastic ordinary differential equations (SODEs) by observing particle ensembles at discrete and sparse time instants, i.e., multiple "snapshots". Particle coordinate…
regressionNeural Jump ODEs as Generative Models
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 ap…