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Identifiability of parameters is an essential property for a statistical model to be useful in most settings. However, establishing parameter identifiability for Bayesian networks with hidden variables remains challenging. In the context of…

Statistics Theory · Mathematics 2014-06-04 Elizabeth S. Allman , John A. Rhodes , Elena Stanghellini , Marco Valtorta

Statistical models can involve implicitly defined quantities, such as solutions to nonlinear ordinary differential equations (ODEs), that unavoidably need to be numerically approximated in order to evaluate the model. The approximation…

Computation · Statistics 2024-09-16 Juho Timonen , Nikolas Siccha , Ben Bales , Harri Lähdesmäki , Aki Vehtari

Neural ordinary differential equations (NODE) have been recently proposed as a promising approach for nonlinear system identification tasks. In this work, we systematically compare their predictive performance with current state-of-the-art…

Machine Learning · Computer Science 2022-03-16 Aowabin Rahman , Ján Drgoňa , Aaron Tuor , Jan Strube

This paper focuses on the problem of quantifying the effects of model-structure uncertainty in the context of time-evolving dynamical systems. This is motivated by multi-model uncertainty in computer physics simulations: developers often…

Dynamical Systems · Mathematics 2019-02-01 Anthony M. DeGennaro , Nathan M. Urban , Balasubramanya T. Nadiga , Terry Haut

This paper presents a novel framework for characterizing dissipativity of uncertain systems whose dynamics evolve according to differential-algebraic equations. Sufficient conditions for dissipativity (specializing to, e.g., stability or…

Systems and Control · Electrical Eng. & Systems 2024-05-13 Emily Jensen , Neelay Junnarkar , Murat Arcak , Xiaofan Wu , Suat Gumussoy

Dynamical systems, prevalent in various scientific and engineering domains, are susceptible to anomalies that can significantly impact their performance and reliability. This paper addresses the critical challenges of anomaly detection,…

Machine Learning · Computer Science 2025-07-18 Yue Sun , Rick S. Blum , Parv Venkitasubramaniam

A novel framework is introduced to formalize identifiability in well-specified but ill-posed linear regression models. The framework is distribution-free and accommodates highly correlated features that may or may not relate to the…

Statistics Theory · Mathematics 2026-03-05 Gianluca Finocchio , Tatyana Krivobokova

We discuss issues of structural and practical identifiability of partially observed differential equations which are often applied in systems biology. The development of mathematical methods to investigate structural non-identifiability has…

The advancement of in-vehicle sensors provides abundant datasets to estimate parameters of car-following models that describe driver behaviors. The question of parameter identifiability of such models (i.e., whether it is possible to infer…

Dynamical Systems · Mathematics 2022-02-21 Yanbing Wang , Maria Laura Delle Monache , Daniel B. Work

Scientists use mathematical modelling to understand and predict the properties of complex physical systems. In highly parameterised models there often exist relationships between parameters over which model predictions are identical, or…

Data Analysis, Statistics and Probability · Physics 2017-03-24 Dhruva V. Raman , James Anderson , Antonis Papachristodoulou

The paper concerns the problem of predicting the effect of actions or interventions on a system from a combination of (i) statistical data on a set of observed variables, and (ii) qualitative causal knowledge encoded in the form of a…

Artificial Intelligence · Computer Science 2012-07-02 Carlos Brito , Judea Pearl

Identifying latent variables and causal structures from observational data is essential to many real-world applications involving biological data, medical data, and unstructured data such as images and languages. However, this task can be…

Machine Learning · Computer Science 2023-11-01 Lingjing Kong , Biwei Huang , Feng Xie , Eric Xing , Yuejie Chi , Kun Zhang

End-to-end learning of dynamical systems with black-box models, such as neural ordinary differential equations (ODEs), provides a flexible framework for learning dynamics from data without prescribing a mathematical model for the dynamics.…

Machine Learning · Statistics 2022-06-20 Paidamoyo Chapfuwa , Sherri Rose , Lawrence Carin , Edward Meeds , Ricardo Henao

Statistical latent class models are widely used in social and psychological researches, yet it is often difficult to establish the identifiability of the model parameters. In this paper we consider the identifiability issue of a family of…

Methodology · Statistics 2016-03-15 Gongjun Xu

Neural ordinary differential equations (ODEs) are an emerging class of deep learning models for dynamical systems. They are particularly useful for learning an ODE vector field from observed trajectories (i.e., inverse problems). We here…

Machine Learning · Computer Science 2023-05-23 Katharina Ott , Michael Tiemann , Philipp Hennig

This paper presents a method for investigating, through an automatic procedure, the (lack of) identifiability of parametrized dynamical models. This method takes into account constraints on parameters and returns parameters whose…

Dynamical Systems · Mathematics 2016-10-11 Nathalie Verdière , Sébastien Orange

Parameter inference and uncertainty quantification are important steps when relating mathematical models to real-world observations, and when estimating uncertainty in model predictions. However, methods for doing this can be…

Quantitative Methods · Quantitative Biology 2025-08-27 Michael J. Plank , Matthew J. Simpson

A lot of information concerning solutions of linear differential equations can be computed directly from the equation. It is therefore natural to consider these equations as a data-structure, from which mathematical properties can be…

Symbolic Computation · Computer Science 2018-11-22 Bruno Salvy

In this paper, we consider to what degree the structure of a linear system is determined by the system's input/output behavior. The structure of a linear system is a directed graph where the vertices represent the variables in the system…

Optimization and Control · Mathematics 2011-09-19 Remco Bras

Structural equation modeling (SEM) is a statistical method widely used in educational research to investigate relationships between variables. SEM models are typically constructed based on theoretical foundations and assessed through fit…

Physics Education · Physics 2024-05-31 Yangqiuting Li , Chandralekha Singh