The state-space models (SSMs) are widely utilized in the analysis of time-series data. SSMs rely on an explicit definition of the state and observation processes. Characterizing these processes is not always easy and becomes a modeling challenge when the dimension of observed data grows or the observed data distribution deviates from the normal distribution. Here, we propose a new formulation of SSM for high-dimensional observation processes. We call this solution the deep direct discriminative decoder (D4). The D4 brings deep neural networks' expressiveness and scalability to the SSM formulation letting us build a novel solution that efficiently estimates the underlying state processes through high-dimensional observation signal. We demonstrate the D4 solutions in simulated and real data such as Lorenz attractors, Langevin dynamics, random walk dynamics, and rat hippocampus spiking neural data and show that the D4 performs better than traditional SSMs and RNNs. The D4 can be applied to a broader class of time-series data where the connection between high-dimensional observation and the underlying latent process is hard to characterize.

翻译：状态空间模型（SSMs）被广泛应用于时间序列数据分析中。SSMs依赖于状态与观测过程的显式定义。然而，当观测数据维数增加或观测数据分布偏离正态分布时，表征这些过程并非易事，并构成建模挑战。本文针对高维观测过程提出了SSM的一种新形式，我们将其命名为深层直接判别解码器（D4）。D4将深度神经网络的表达力与可扩展性引入SSM框架，使我们能够构建高效估计高维观测信号下潜在状态过程的新型解决方案。我们在洛伦兹吸引子、朗之万动力学、随机游走动力学以及大鼠海马体尖峰神经数据等模拟与真实数据上验证了D4方案，结果表明D4优于传统SSMs和RNNs。对于高维观测与潜在隐过程之间关联难以刻画的一类更广泛的时间序列数据，D4亦具有适用性。