We propose a new variational inference algorithm for learning in Gaussian Process State-Space Models (GPSSMs). Our algorithm enables learning of unstable and partially observable systems, where previous algorithms fail. Our main algorithmic contribution is a novel approximate posterior that can be calculated efficiently using a single forward and backward pass along the training trajectories. The forward-backward pass is inspired on Kalman smoothing for linear dynamical systems but generalizes to GPSSMs. Our second contribution is a modification of the conditioning step that effectively lowers the Kalman gain. This modification is crucial to attaining good test performance where no measurements are available. Finally, we show experimentally that our learning algorithm performs well in stable and unstable real systems with hidden states.
翻译:我们提议在高山进程国家空间模型(GPSSM)中采用新的变式推论算法进行学习。我们的算法使得能够学习不稳定和部分可观测的系统,而先前的算法失败了。我们的主要算法贡献是一个新颖的近似后方,可以通过在训练轨迹上的单个前向和后向传递来有效计算。前向传球的灵感来自卡尔曼为线性动态系统平滑,但泛泛地为GPSMS。我们的第二个贡献是修改使Kalman受益率降低的调节步骤。这一修改对于在没有测量的情况下取得良好的测试性能至关重要。最后,我们实验地显示,我们的学习算法在稳定、不稳定的、隐藏状态下运行良好。