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Paper · 2105.02522 · 2021

Neural graphical modelling in continuous-time: consistency guarantees and algorithms

arXiv · PDF · Open in the Atlas

Code that ran

We lifted 9 functions out of this paper's own repositories and ran 9 of them in a sandbox. "Ran" means the function executed on a synthesized input and returned a value. It is not a reproduction of the paper's results.

RepositoryRoleRan
alexisbellot/Graphical-modelling-continuous-time pwc_unofficial 9 of 9
FunctionStatusWhere it lives
activation_helper Ran alexisbellot/Graphical-modelling-continuous-time/model_helper.py
code served (permissive licence) · get_code("8f5922d83d039372")
compute_derivatives Ran alexisbellot/Graphical-modelling-continuous-time/utils.py
code served (permissive licence) · get_code("f5758e099543025e")
compute_spline Ran alexisbellot/Graphical-modelling-continuous-time/utils.py
code served (permissive licence) · get_code("dd38b21ec91440d2")
make_var_stationary Ran alexisbellot/Graphical-modelling-continuous-time/utils.py
code served (permissive licence) · get_code("3a98557267414e0c")
regularize Ran alexisbellot/Graphical-modelling-continuous-time/benchmarks/clstm.py
code served (permissive licence) · get_code("567bcdd840d7c476")
regularize Ran alexisbellot/Graphical-modelling-continuous-time/benchmarks/cmlp.py
code served (permissive licence) · get_code("39d3ee9cc2219f50")
ridge_regularize Ran alexisbellot/Graphical-modelling-continuous-time/benchmarks/clstm.py
code served (permissive licence) · get_code("d8f9397ba628e2f1")
squared_loss Ran alexisbellot/Graphical-modelling-continuous-time/NMC.py
code served (permissive licence) · get_code("c60cc034e8957e26")
train_model_gista Ran alexisbellot/Graphical-modelling-continuous-time/benchmarks/clstm.py
code served (permissive licence) · get_code("cef41e323886a2ff")

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Abstract

The discovery of structure from time series data is a key problem in fields of study working with complex systems. Most identifiability results and learning algorithms assume the underlying dynamics to be discrete in time. Comparatively few, in contrast, explicitly define dependencies in infinitesimal intervals of time, independently of the scale of observation and of the regularity of sampling. In this paper, we consider score-based structure learning for the study of dynamical systems. We prove that for vector fields parameterized in a large class of neural networks, least squares optimization with adaptive regularization schemes consistently recovers directed graphs of local independencies in systems of stochastic differential equations. Using this insight, we propose a score-based learning algorithm based on penalized Neural Ordinary Differential Equations (modelling the mean process) that we show to be applicable to the general setting of irregularly-sampled multivariate time series and to outperform the state of the art across a range of dynamical systems.

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