DeepBayes -- an estimator for parameter estimation in stochastic nonlinear dynamical models
This work addresses a challenging computational bottleneck in parameter estimation for stochastic nonlinear dynamical systems, with potential applications in real-world domains like engineering and science, though it appears incremental as it builds on existing neural network techniques.
The authors tackled the problem of estimating unknown parameters in stochastic nonlinear dynamical models, which is computationally intensive with existing methods, by proposing DeepBayes estimators using deep recurrent neural networks. The result is an approach that achieves asymptotic performance comparable to the Bayes estimator while offering significant time savings during inference.
Stochastic nonlinear dynamical systems are ubiquitous in modern, real-world applications. Yet, estimating the unknown parameters of stochastic, nonlinear dynamical models remains a challenging problem. The majority of existing methods employ maximum likelihood or Bayesian estimation. However, these methods suffer from some limitations, most notably the substantial computational time for inference coupled with limited flexibility in application. In this work, we propose DeepBayes estimators that leverage the power of deep recurrent neural networks in learning an estimator. The method consists of first training a recurrent neural network to minimize the mean-squared estimation error over a set of synthetically generated data using models drawn from the model set of interest. The a priori trained estimator can then be used directly for inference by evaluating the network with the estimation data. The deep recurrent neural network architectures can be trained offline and ensure significant time savings during inference. We experiment with two popular recurrent neural networks -- long short term memory network (LSTM) and gated recurrent unit (GRU). We demonstrate the applicability of our proposed method on different example models and perform detailed comparisons with state-of-the-art approaches. We also provide a study on a real-world nonlinear benchmark problem. The experimental evaluations show that the proposed approach is asymptotically as good as the Bayes estimator.