Deep Discriminative Direct Decoders for High-dimensional Time-series Analysis

Dynamical latent variable modeling has been significantly invested over the last couple of decades with established solutions encompassing generative processes like the state-space model (SSM) and discriminative processes like a recurrent or a deep neural network (DNN). These solutions are powerful tools with promising results; however, surprisingly they were never put together in a unified model to analyze complex multivariate time-series data. A very recent modeling approach, called the direct discriminative decoder (DDD) model, proposes a principal solution to combine SMM and DNN models, with promising results in decoding underlying latent processes, e.g. rat movement trajectory, through high-dimensional neural recordings. The DDD consists of a) a state transition process, as per the classical dynamical models, and b) a discriminative process, like DNN, in which the conditional distribution of states is defined as a function of the current observations and their recent history. Despite promising results of the DDD model, no training solutions, in the context of DNN, have been utilized for this model. Here, we propose how DNN parameters along with an optimal history term can be simultaneously estimated as a part of the DDD model. We use the D4 abbreviation for a DDD with a DNN as its discriminative process. We showed the D4 decoding performance in both simulation and (relatively) high-dimensional neural data. In both datasets, D4 performance surpasses the state-of-art decoding solutions, including those of SSM and DNNs. The key success of DDD and potentially D4 is efficient utilization of the recent history of observation along with the state-process that carries long-term information, which is not addressed in either SSM or DNN solutions. We argue that D4 can be a powerful tool for the analysis of high-dimensional time-series data.