From Deterministic ODEs to Dynamic Structural Causal Models

Rubenstein, Paul K.; Bongers, Stephan; Schoelkopf, Bernhard; Mooij, Joris M.

doi:10.48550/arxiv.1608.08028

Cited by 5 publications

(6 citation statements)

References 2 publications

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“…As the authors in Aalen et al ( 2012) suggested, differential equations allow for a natural interpretation of causality in dynamic systems. The authors in (Mooij et al, 2013;Rubenstein et al, 2016;Bongers and Mooij, 2018) built an explicit bridge between the differential equations and the causal models by establishing the relationship between ODEs/Random Differential Equations (RDEs) and structural causal models. Hansen and Sokol provided a causal interpretation of Stochastic Differential Equations (SDEs) Hansen and Sokol (2014).…”

Section: Connection Between Causality and Differential Equationsmentioning

confidence: 99%

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Identifiability and Asymptotics in Learning Homogeneous Linear ODE Systems from Discrete Observations

Wang¹,

Huang²,

Gong³

et al. 2022

Preprint

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Ordinary Differential Equations (ODEs) have recently gained a lot of attention in machine learning. However, the theoretical aspects, e.g., identifiability and asymptotic properties of statistical estimation are still obscure. This paper derives a sufficient condition for the identifiability of homogeneous linear ODE systems from a sequence of equally-spaced error-free observations sampled from a single trajectory. When observations are disturbed by measurement noise, we prove that under mild conditions, the parameter estimator based on the Nonlinear Least Squares (NLS) method is consistent and asymptotic normal with n −1/2 convergence rate. Based on the asymptotic normality property, we construct confidence sets for the unknown system parameters and propose a new method to infer the causal structure of the ODE system, i.e., inferring whether there is a causal link between system variables. Furthermore, we extend the results to degraded observations, including aggregated and time-scaled ones. To the best of our knowledge, our work is the first systematic study of the identifiability and asymptotic properties in learning linear ODE systems. We also construct simulations with various system dimensions to illustrate the established theoretical results.

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Section: Connection Between Causality and Differential Equationsmentioning

confidence: 99%

“…For instance, ODEs have been used to build new families of deep neural networks (Chen et al, 2018;Yan et al, 2019;Zhang et al, 2019) and the connection between ODEs and structural causal models has been established (Mooij et al, 2013;Rubenstein et al, 2016).…”

Section: Introductionmentioning

confidence: 99%

Identifiability and Asymptotics in Learning Homogeneous Linear ODE Systems from Discrete Observations

Wang¹,

Huang²,

Gong³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…Continuous-time Bayesian networks further adapted the idea to modeling cause-effect relationships in time-continuous processes (Gopalratnam et al, 2005, Nodelman et al, 2002, Nodelman, 2007. A different approach for causal modeling of time-continuous processes is to learn ODEs, which under certain conditions imply a structured causal model (Rubenstein et al, 2016). zIn this work, we describe a class of continuous models that has the ability to account for interventions and therefore captures the causal structures from data.…”

Section: Related Workmentioning

confidence: 99%

Causal Navigation by Continuous-time Neural Networks

Vorbach,

Hasani,

Amini

et al. 2021

Preprint

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Imitation learning enables high-fidelity, vision-based learning of policies within rich, photorealistic environments. However, such techniques often rely on traditional discrete-time neural models and face difficulties in generalizing to domain shifts by failing to account for the causal relationships between the agent and the environment. In this paper, we propose a theoretical and experimental framework for learning causal representations using continuous-time neural networks, specifically over their discrete-time counterparts. We evaluate our method in the context of visual-control learning of drones over a series of complex tasks, ranging from short-and long-term navigation, to chasing static and dynamic objects through photorealistic environments. Our results demonstrate that causal continuous-time deep models can perform robust navigation tasks, where advanced recurrent models fail. These models learn complex causal control representations directly from raw visual inputs and scale to solve a variety of tasks using imitation learning.

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“…A lot of work [47,31,41,10,27,55] has been dedicated to interpreting ordinary differential equations as structural causal models and consequently the associated task of intervening therein. More precisely, attention has been placed on extending causal theory [45,52] to the cyclic case, thereby enabling causal modelling of systems that involve feedback [41,33,17,42,30,49,47].…”

Section: E7 Real-world Economic Data (Econ)mentioning

confidence: 99%

Dynamic Causal Bayesian Optimization

Aglietti¹,

Dhir²,

González³

et al. 2021

Preprint

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This paper studies the problem of performing a sequence of optimal interventions in a causal dynamical system where both the target variable of interest and the inputs evolve over time. This problem arises in a variety of domains e.g. system biology and operational research. Dynamic Causal Bayesian Optimization (DCBO) brings together ideas from sequential decision making, causal inference and Gaussian process (GP) emulation. DCBO is useful in scenarios where all causal effects in a graph are changing over time. At every time step DCBO identifies a local optimal intervention by integrating both observational and past interventional data collected from the system. We give theoretical results detailing how one can transfer interventional information across time steps and define a dynamic causal GP model which can be used to quantify uncertainty and find optimal interventions in practice. We demonstrate how DCBO identifies optimal interventions faster than competing approaches in multiple settings and applications.

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From Deterministic ODEs to Dynamic Structural Causal Models

Cited by 5 publications

References 2 publications

Identifiability and Asymptotics in Learning Homogeneous Linear ODE Systems from Discrete Observations

Identifiability and Asymptotics in Learning Homogeneous Linear ODE Systems from Discrete Observations

Causal Navigation by Continuous-time Neural Networks

Dynamic Causal Bayesian Optimization

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