论文标题
部分可观测时空混沌系统的无模型预测
Amortized backward variational inference in nonlinear state-space models
论文作者
论文摘要
我们考虑使用变异推理中一般状态空间模型中的状态估计问题。对于使用与实际关节平滑分布相同的向后分解定义的通用变异家族，我们首次确定，在混合假设下，添加态函数期望的变异近似近似是在观察次数中最线性地呈现的误差。 此保证与已知的上限是使用标准蒙特卡洛方法近似平滑分布的上限。此外，我们提出了一个摊销的推理框架，其中神经网络在任何时候共享的步骤都输出变分内核的参数。我们还研究了经验参数化，从而允许分析分布的分析边缘化，从而导致有效的平滑算法。 对最先进的变化解决方案进行了重大改进，尤其是当生成模型取决于强烈的非线性和非注入性混合函数时。
We consider the problem of state estimation in general state-space models using variational inference. For a generic variational family defined using the same backward decomposition as the actual joint smoothing distribution, we establish for the first time that, under mixing assumptions, the variational approximation of expectations of additive state functionals induces an error which grows at most linearly in the number of observations. This guarantee is consistent with the known upper bounds for the approximation of smoothing distributions using standard Monte Carlo methods. Moreover, we propose an amortized inference framework where a neural network shared over all times steps outputs the parameters of the variational kernels. We also study empirically parametrizations which allow analytical marginalization of the variational distributions, and therefore lead to efficient smoothing algorithms. Significant improvements are made over state-of-the art variational solutions, especially when the generative model depends on a strongly nonlinear and noninjective mixing function.
