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Latent variable models have been widely applied for the analysis of timeseries resulting from experimental neuroscience techniques. In these datasets,observations are relatively smooth and possibly nonlinear. We presentVariational Inference for Nonlinear Dynamics (VIND), a variational inferenceframework that is able to uncover nonlinear, smooth latent dynamics fromsequential data. The framework is a direct extension of PfLDS; including astructured approximate posterior describing spatially-dependent lineardynamics, as well as an algorithm that relies on the fixed-point iterationmethod to achieve convergence. We apply VIND to electrophysiology, single-cellvoltage and widefield imaging datasets with state-of-the-art results inreconstruction error. In single-cell voltage data, VIND finds a 5D latentspace, with variables akin to those of Hodgkin-Huxley-like models. VIND'slearned dynamics are further quantified by predicting future neural activity.VIND excels in this task, in some cases substantially outperforming currentmethods.

Nonlinear Evolution via Spatially-Dependent Linear Dynamics for Electrophysiology and Calcium Data