Neural graphical modelling in continuous-time: consistency guarantees and algorithms
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.
Code (2)
Tasks
Causal DiscoveryGraph LearningTime SeriesTime Series AnalysisSimilar Papers 제목 키워드 기반
Provable Computational and Statistical Guarantees for Efficient Learning of Continuous-Action Graphical Games
In this paper, we study the problem of learning the set of pure strategy Nash equilibria and the exact structure of a continuous-action graphical game with quadratic payoffs by observing a small set of perturbed equilibr…
Distributionally Robust Graphical Models
In many structured prediction problems, complex relationships between variables are compactly defined using graphical structures. The most prevalent graphical prediction methods---probabilistic graphical models and large…
PredictionStructured PredictionDistributed Parameter Estimation in Probabilistic Graphical Models
This paper presents foundational theoretical results on distributed parameter estimation for undirected probabilistic graphical models. It introduces a general condition on composite likelihood decompositions of these mo…
parameter estimationProvable Sample Complexity Guarantees for Learning of Continuous-Action Graphical Games with Nonparametric Utilities
In this paper, we study the problem of learning the exact structure of continuous-action games with non-parametric utility functions. We propose an $\ell_1$ regularized method which encourages sparsity of the coefficient…
Continuous Inference in Graphical Models with Polynomial Energies
In this paper, we tackle the problem of performing inference in graphical models whose energy is a polynomial function of continuous variables. Our energy minimization method follows a dual decomposition approach, where …
Diversity