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 the modelling of 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.

翻译：变分推断的进展为贝叶斯估计问题提供了有前景的路径。这些进展使变分系统发育推断成为马尔可夫链蒙特卡洛方法在近似系统发育后验分布时的替代方案。然而，此类方法的主要缺陷之一在于通过固定分布对先验进行建模——若该分布偏离当前数据分布，则可能导致后验近似产生偏差。本文提出一种方法及实现框架，通过基于梯度的优化与神经网络参数化技术学习先验密度参数，以缓解先验密度的僵化性。我们将该方法应用于多个马尔可夫链置换模型下的分支长度与进化参数估计。仿真实验结果表明，该方法在估计分支长度与进化模型参数方面表现优异，同时证明灵活的先验模型比预定义先验模型能获得更优结果。最后，研究结果突显了神经网络在优化先验密度参数初始化过程中的有效性。