Gradient-based Bayesian Experimental Design for Implicit Models using Mutual Information Lower Bounds

We introduce a framework for Bayesian experimental design (BED) with implicit\nmodels, where the data-generating distribution is intractable but sampling from\nit is still possible. In order to find optimal experimental designs for such\nmodels, our approach maximises mutual information lower bounds that are\nparametrised by neural networks. By training a neural network on sampled data,\nwe simultaneously update network parameters and designs using stochastic\ngradient-ascent. The framework enables experimental design with a variety of\nprominent lower bounds and can be applied to a wide range of scientific tasks,\nsuch as parameter estimation, model discrimination and improving future\npredictions. Using a set of intractable toy models, we provide a comprehensive\nempirical comparison of prominent lower bounds applied to the aforementioned\ntasks. We further validate our framework on a challenging system of stochastic\ndifferential equations from epidemiology.\n