Title: Preferential dynamic modeling with forward-backward smoothing
Primary area: applications to neuroscience & cognitive science
Keywords: Subspace identification, Dynamical modeling, Neuroscience, RNN, Supervised learning

Abstract: Estimating a secondary signal (e.g., behavior) from neural activity over time is central to both causal online decoding and non-causal offline inference in neuroscience. Existing two-signal latent state-space modeling methods typically either support causal prediction of the secondary signal from the primary signal or non-causal inference (smoothing), but rarely both; here we extend one analytical linear method (PSID) and one nonlinear deep learning method (DPAD) beyond causal prediction to also support non-causal inference, yielding a more universally applicable family of methods for diverse applications. We provide theoretical derivations extending PSID to enable optimal filtering (i.e., estimate sample $k$ given samples $1$ to $k$) and optimal smoothing (i.e., estimate sample k given samples $1$ to $N$, where $N > k$) of the secondary signal. We show that, in the PSID setting, the presence of a secondary signal increases identifiability. This allows us to uniquely learn the quantities needed for the optimal Kalman update via a reduced-rank regression step that augments the standard SVD-based PSID algorithm, yielding our first contribution, PSID with filtering. We next design a forward-backward construction for smoothing, yielding our second contribution, PSID with smoothing. For nonlinear prioritized modeling, we extend DPAD to a bidirectional variant that combines forward and backward hidden states at readout to perform smoothing, yielding our third contribution, DPAD with smoothing. In simulations, we validate that PSID with filtering and smoothing reach ideal performance. In non-human primate motor cortex data, PSID with smoothing consistently improves over PSID with filtering, which improves over one-step-ahead prediction with standard PSID, with all three cases outperforming a linear neural dynamic modeling (NDM) baseline. Finally, we test DPAD with smoothing on three Neural Latents Benchmark (NLB) datasets, where it achieves the top behavior-decoding result on at least one dataset and near-top performance in behavior decoding and held-out neural prediction on all three. Together, these methods form a family with wide-ranging applications, from causal online decoding to offline inference, in both linear and nonlinear settings.