Existing deterministic variational inference approaches for diffusion processes use simple proposals and target the marginal density of the posterior. We construct the variational process as a controlled version of the prior process and approximate the posterior by a set of moment functions. In combination with moment closure, the smoothing problem is reduced to a deterministic optimal control problem. Exploiting the path-wise Fisher information, we propose an optimization procedure that corresponds to a natural gradient descent in the variational parameters. Our approach allows for richer variational approximations that extend to state-dependent diffusion terms. The classical Gaussian process approximation is recovered as a special case.
翻译:现有扩散过程的确定性差异推论方法使用简单的建议,针对后方的边际密度。我们将变异过程构建为先前过程的受控版本,并以一组瞬间函数近似于后方。随着时间的结束,平滑问题被降为确定性的最佳控制问题。利用路由的渔业信息,我们建议一种与变异参数中自然梯度下降相对应的优化程序。我们的方法允许更丰富的变异近似值,以扩展到依赖国家的传播条件。古典高斯近似值作为一个特殊案例被恢复。