Reproduce “Nonlinear Evolution via Spatially-Dependent Linear Dynamics for Electrophysiology and Calcium Data” on OpenResearch

About this paper

Daniel Hernandez, Antonio Khalil Moretti, Ziqiang Wei, Shreya Saxena, John Cunningham, Liam Paninski

VIND models single-cell voltage recordings with nonlinear latent dynamics that continue generating activity after observations stop. It uses the same evolution rule in its generative and recognition models, approximating an intractable posterior with a Gaussian. In five dimensions, VIND achieved an order-of-magnitude advantage over GfLDS on forward interpolation. Its starting state is inferred from the full sequence, not past-only data.

Key insights

• A flexible variational inference framework can be constructed to leverage the generative model's nonlinear dynamics directly in the approximate posterior, even if the posterior is initially intractable.
• Approximating an intractable posterior with a tractable Gaussian via Laplace approximation and fixed-point iteration provides a robust and efficient mechanism for learning complex nonlinear dynamics.
• The use of state-dependent linear dynamics ($A(z)z$) within the generative model allows for capturing complex nonlinear behavior while maintaining computational efficiency for posterior inference.

Summary by alphaXiv.