Efficient Amortised Bayesian Inference for Hierarchical and Nonlinear Dynamical Systems (1905.12090v2)

Abstract: We introduce a flexible, scalable Bayesian inference framework for nonlinear dynamical systems characterised by distinct and hierarchical variability at the individual, group, and population levels. Our model class is a generalisation of nonlinear mixed-effects (NLME) dynamical systems, the statistical workhorse for many experimental sciences. We cast parameter inference as stochastic optimisation of an end-to-end differentiable, block-conditional variational autoencoder. We specify the dynamics of the data-generating process as an ordinary differential equation (ODE) such that both the ODE and its solver are fully differentiable. This model class is highly flexible: the ODE right-hand sides can be a mixture of user-prescribed or "white-box" sub-components and neural network or "black-box" sub-components. Using stochastic optimisation, our amortised inference algorithm could seamlessly scale up to massive data collection pipelines (common in labs with robotic automation). Finally, our framework supports interpretability with respect to the underlying dynamics, as well as predictive generalization to unseen combinations of group components (also called "zero-shot" learning). We empirically validate our method by predicting the dynamic behaviour of bacteria that were genetically engineered to function as biosensors. Our implementation of the framework, the dataset, and all code to reproduce the experimental results is available at https://www.github.com/Microsoft/vi-hds .

• The paper presents VI-HDS, a Bayesian inference framework using block-conditional variational autoencoders for efficient parameter estimation.
• It employs differentiable ODEs to model hierarchical dynamics, enabling accurate zero-shot predictions in synthetic biological systems.
• The framework achieves competitive performance with reduced computation time compared to traditional MCMC methods.

Efficient Amortised Bayesian Inference for Hierarchical and Nonlinear Dynamical Systems

The paper presents a scalable Bayesian inference framework specifically designed for nonlinear dynamical systems exhibiting hierarchical variability across individual, group, and population levels. The authors extend nonlinear mixed-effects dynamical systems models into a flexible inference framework leveraging stochastic optimization through variational autoencoders. This approach aligns with advancements in machine learning, embracing scalable statistical modeling in synthetic biology and beyond.

Methodology Overview

Central to the proposed framework, VI-HDS (Variational Inference for Hierarchical Dynamical Systems), is the use of a block-conditional variational autoencoder to carry out parameter inference, which allows for hierarchical organization and decomposition. The formulation of the model involves specifying data-generating processes via ordinary differential equations (ODEs) that are designed to be fully differentiable, both structurally and solution-wise. This ensures that the model is not only generalizable but also accommodates both white-box (mechanistically prescribed) and black-box (neural network approximations) components.

The model supports interpretability and zero-shot learning capabilities, evidencing the ability to extrapolate to unseen group-component combinations. Empirical validation is demonstrated using a synthetic biology application, where the dynamic behavior of genetically engineered bacteria used as biosensors is modeled. The results illustrate the framework’s ability to predict biological device responses with remarkable precision and accuracy.

Implementation and Results

The experimental application on synthetic biological systems demonstrates the efficiency of the proposed framework. The paper reports that VI-HDS performs comparably to state-of-the-art methods while offering a significant reduction in computation time, especially compared to traditional methods like Markov Chain Monte Carlo (MCMC) which are computationally intensive. Specifically, the framework exhibits robust scalability conducive to high-dimensional data environments commonly found in automated laboratory settings.

In one such experiment, the authors hold out one device combination while training on others, successfully predicting the held-out device’s behavior. This ability speaks to the promise of VI-HDS in synthetic constructs where components are readily exchangeable and combinatorially complex, underscoring the model’s potential in advancing biological design and innovation.

Implications and Future Directions

The theoretical and practical implications of this research underscore a dynamic shift in Bayesian modeling of hierarchical and complex systems. By integrating mechanistic insights with deep learning architectures, the framework paves the way for more efficient hypothesis testing and parameter estimation in data-intensive domains. The future prospects entail extending these methods to encompass stochastic dynamical systems, thereby enhancing their utility in broader real-world scenarios.

Furthermore, the integration of active learning paradigms within this framework holds potential in driving autonomous exploration and optimization in experimental biology and chemistry. Overall, the research advances the statistical toolkit available for complex system modeling, providing a foundation for continued exploration and application in diverse scientific fields.