We introduce an amortized variational inference algorithm and structured variational approximation for state-space models with nonlinear dynamics driven by Gaussian noise. Importantly, the proposed framework allows for efficient evaluation of the ELBO and low-variance stochastic gradient estimates without resorting to diagonal Gaussian approximations by exploiting (i) the low-rank structure of Monte-Carlo approximations to marginalize the latent state through the dynamics (ii) an inference network that approximates the update step with low-rank precision matrix updates (iii) encoding current and future observations into pseudo observations -- transforming the approximate smoothing problem into an (easier) approximate filtering problem. Overall, the necessary statistics and ELBO can be computed in $O(TL(Sr + S^2 + r^2))$ time where $T$ is the series length, $L$ is the state-space dimensionality, $S$ are the number of samples used to approximate the predict step statistics, and $r$ is the rank of the approximate precision matrix update in the update step (which can be made of much lower dimension than $L$).

引入一种基于分级变分推断和结构化变分逼近的摊还推断算法，应用于受高斯噪声驱动的非线性动力学状态空间模型。通过利用蒙特卡洛逼近方法中的低秩结构来辅助隐变量的边际化计算、基于低秩精度矩阵更新的推断网络来近似更新步骤、并将当前和未来的观测数据转化为伪观测数据，从而将近似平滑问题转化为（更易解决的）近似过滤问题。整个计算过程的时间复杂度为$O(TL(Sr + S^2 + r^2))$，其中$T$为时间序列长度，$L$为状态空间维度，$S$为用于近似预测步骤的样本数，$r$为近似精度矩阵更新的秩（远远小于$L$维）。

大规模变分高斯状态空间模型