Variational Inference for Linear Systems with Latent Parameter Space

We present a method to perform identification of systems with external inputs whose parameters are indexed by a lower-dimensional latent space. We apply a variational Bayes inference method to approximate the posterior distribution of the system parameters and latent variables, given input and output measurements. This approach seeks to minimize the Kullback-Leibler divergence between the full (but intractable) posterior distribution of the parameters and an approximating (yet tractable) factorized distribution. The method enables inference for systems whose parameters are subject to latent sources of variation, and therefore constitutes a relevant tool for modeling and control in complex domains, such as biological systems and neuroscience.