  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.
