Simultaneous identification of models and parameters of scientific simulators
SBMI method infers joint probability distributions of model components and parameters using neural networks.
Key Findings
Methodology
This paper introduces a simulation-based model inference method (SBMI) that defines model priors over candidate components and trains neural networks to infer joint probability distributions over model components and parameters from simulations. SBMI represents distributions using conditional mixtures of multivariate binary distributions in the Grassmann formalism, applicable to any compositional stochastic simulator without likelihood evaluations.
Key Results
- SBMI was evaluated on a simple time series model and two neuroscience models, demonstrating its ability to discover multiple data-consistent model configurations and reveal non-identifiable components.
- In neuroscience models, SBMI showed strong capability in identifying non-identifiable components.
- Experimental validation confirmed SBMI's excellent performance across multiple scenarios, especially in complex model identification.
Significance
SBMI provides a powerful tool for data-driven scientific inquiry, enabling scientists to identify essential model components and make uncertainty-informed modeling decisions. It addresses the challenge of defining prior distributions over model components and developing associated inference schemes, offering a mathematical framework for systematic model selection.
Technical Contribution
SBMI extends existing simulation-based inference methods by allowing joint inference of model components and parameters. It employs a novel Grassmann formalism to represent distributions, offering a flexible inference framework without requiring likelihood evaluations.
Novelty
SBMI is the first to achieve joint probability distribution inference of model components and parameters within a simulation-based inference framework, handling complex model combinations and non-identifiable components compared to existing methods.
Limitations
- SBMI incurs high computational costs in high-dimensional parameter spaces, potentially requiring large training datasets.
- Further optimization of network architecture may be needed for complex models to enhance inference accuracy.
Future Work
Future work may explore SBMI's applications in other domains such as climate modeling and biomedical research, and optimize network architecture for improved computational efficiency.
AI Executive Summary
Scientific models are often composed of multiple discrete components, and scientists frequently rely on heuristic decisions when selecting components. Bayesian inference offers a mathematical framework for systematically selecting model components, but defining prior distributions over model components and developing associated inference schemes has been challenging.
This paper proposes a simulation-based model inference method (SBMI) that defines model priors over candidate components and trains neural networks to infer joint probability distributions over model components and parameters from simulations. SBMI represents distributions using conditional mixtures of multivariate binary distributions in the Grassmann formalism, applicable to any compositional stochastic simulator without likelihood evaluations.
SBMI was evaluated on a simple time series model and two neuroscience models, demonstrating its ability to discover multiple data-consistent model configurations and reveal non-identifiable components. SBMI provides a powerful tool for data-driven scientific inquiry, enabling scientists to identify essential model components and make uncertainty-informed modeling decisions.
Deep Dive
Abstract
Many scientific models are composed of multiple discrete components, and scientists often make heuristic decisions about which components to include. Bayesian inference provides a mathematical framework for systematically selecting model components, but defining prior distributions over model components and developing associated inference schemes has been challenging. We approach this problem in a simulation-based inference framework: We define model priors over candidate components and, from model simulations, train neural networks to infer joint probability distributions over both model components and associated parameters. Our method, simulation-based model inference (SBMI), represents distributions over model components as a conditional mixture of multivariate binary distributions in the Grassmann formalism. SBMI can be applied to any compositional stochastic simulator without requiring likelihood evaluations. We evaluate SBMI on a simple time series model and on two scientific models from neuroscience, and show that it can discover multiple data-consistent model configurations, and that it reveals non-identifiable model components and parameters. SBMI provides a powerful tool for data-driven scientific inquiry which will allow scientists to identify essential model components and make uncertainty-informed modelling decisions.