Prior Density Learning in Variational Bayesian Phylogenetic Parameters Inference

The advances in variational inference are providing promising paths in Bayesian estimation problems. These advances make variational phylogenetic inference an alternative approach to Markov Chain Monte Carlo methods for approximating the phylogenetic posterior. However, one of the main drawbacks of such approaches is modelling the prior through fixed distributions, which could bias the posterior approximation if they are distant from the current data distribution. In this paper, we propose an approach and an implementation framework to relax the rigidity of the prior densities by learning their parameters using a gradient-based method and a neural network-based parameterization. We applied this approach for branch lengths and evolutionary parameters estimation under several Markov chain substitution models. The results of performed simulations show that the approach is powerful in estimating branch lengths and evolutionary model parameters. They also show that a flexible prior model could provide better results than a predefined prior model. Finally, the results highlight that using neural networks improves the initialization of the optimization of the prior density parameters.