Learning Networks of Stochastic Differential Equations
We consider linear models for stochastic dynamics. Any such model can be associated a network (namely a directed graph) describing which degrees of freedom interact under the dynamics. We tackle the problem of learning such a network from observation of the system trajectory over a time interval T. We analyse the l1-regularized least squares algorithm and, in the setting in which the underlying network is sparse, we prove performance guarantees that are uniform in the sampling rate as long as this is sufficiently high. This result substantiates the notion of a well defined ‘time complexity’ for the network inference problem.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Universal approximation property of neural stochastic differential equations
We identify various classes of neural networks that are able to approximate continuous functions locally uniformly subject to fixed global linear growth constraints. For such neural networks the associated neural stochas…
Scalable Gradients for Stochastic Differential Equations
The adjoint sensitivity method scalably computes gradients of solutions to ordinary differential equations. We generalize this method to stochastic differential equations, allowing time-efficient and constant-memory comp…
SensitivityVariational InferenceVideo PredictionDeep Forward-Backward SDEs for Min-max Control
This paper presents a novel approach to numerically solve stochastic differential games for nonlinear systems. The proposed approach relies on the nonlinear Feynman-Kac theorem that establishes a connection between parab…
Set-Valued Risk Measures as Backward Stochastic Difference Inclusions and Equations
Scalar dynamic risk measures for univariate positions in continuous time are commonly represented as backward stochastic differential equations. In the multivariate setting, dynamic risk measures have been defined and st…
DiffEqFlux.jl - A Julia Library for Neural Differential Equations
DiffEqFlux.jl is a library for fusing neural networks and differential equations. In this work we describe differential equations from the viewpoint of data science and discuss the complementary nature between machine le…
BIG-bench Machine Learning