Ensemble Kalman Variational Objectives: Nonlinear Latent Trajectory Inference with A Hybrid of Variational Inference and Ensemble Kalman Filter

Latent trajectory inference is a crucial problem within time-series machine learning because the identification immediately provides the interpretability of given data and the relevant systems. Some real-world data such as sequential activity of thousands of neurons [51] have higher dimension than the intrinsic dimension. Other data have lower dimension such as electrophysiological data of voltage measurements in single cells [28]. The latter problem is harder than the former because the observations may be insufficient to describe its dynamics, thus the present paper focuses on this problem to show an advantage of our method. Modeling with latent variables by neural networks have been researched after Recurrent Neural Network [53, 30] was proposed. RNN and its variants (RNNs) such as GRU [9] and LSTM [26] are the benchmark models to learn latent trajectory as the sequence of hidden units to predict or classify the observations.