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Abstract We describe a stochastic, dynamical system capable of inference and learning in a probabilistic latent variable model. The most challenging problem in such models—sampling the posterior distribution over latent variables—is proposed to be solved by harnessing natural sources of stochasticity inherent in electronic and neural systems. We demonstrate this idea for a sparse coding model by deriving a continuous-time equation for inferring its latent variables via Langevin dynamics. The model parameters are learned by simultaneously evolving according to another continuous-time equation, thus bypassing the need for digital accumulators or a global clock. Moreover, we show that Langevin dynamics lead to an efficient procedure for sampling from the posterior distribution in the L0 sparse regime, where latent variables are encouraged to be set to zero as opposed to having a small L1 norm. This allows the model to properly incorporate the notion of sparsity rather than having to resort to a relaxed version of sparsity to make optimization tractable. Simulations of the proposed dynamical system on both synthetic and natural image data sets demonstrate that the model is capable of probabilistically correct inference, enabling learning of the dictionary as well as parameters of the prior.
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Incorporating Deep Learning Into System Dynamics: Amortized Bayesian Inference for Scalable Likelihood‐Free Parameter Estimation
ABSTRACT Estimating parameters and their credible intervals for complex system dynamics models is challenging but critical to continuous model improvement and reliable communication with an increasing fraction of audiences. The purpose of this study is to integrate Amortized Bayesian Inference (ABI) methods with system dynamics. Utilizing Neural Posterior Estimation (NPE), we train neural networks using synthetic data (pairs of ground truth parameters and outcome time series) to estimate parameters of system dynamics models. We apply this method to two example models: a simple Random Walk model and a moderately complex SEIRb model. We show that the trained neural networks can output the posterior for parameters instantly given new unseen time series data. Our analysis highlights the potential of ABI to facilitate a principled, scalable, and likelihood‐free inference workflow that enhance the integration of models of complex systems with data. Accompanying code streamlines application to diverse system dynamics models.
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- Award ID(s):
- 2229819
- PAR ID:
- 10576818
- Publisher / Repository:
- Wiley Blackwell (John Wiley & Sons)
- Date Published:
- Journal Name:
- System Dynamics Review
- Volume:
- 41
- Issue:
- 1
- ISSN:
- 0883-7066
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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