Nonlinear Evolution via Spatially-Dependent Linear Dynamics for Electrophysiology and Calcium Data
Nonlinear Evolution via Spatially-Dependent Linear Dynamics for Electrophysiology and Calcium Data
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发表时间：
2018-11
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通讯作者：
Daniel Hernandez;A. Moretti;S. Saxena;Ziqiang Wei;J. Cunningham;L. Paninski
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作者：
Daniel Hernandez;A. Moretti;S. Saxena;Ziqiang Wei;J. Cunningham;L. Paninski
潜变量模型已被广泛应用于实验神经科学技术所产生的时间序列的分析和可视化。这些数据集的观测结果的演变相对平滑，可能是非线性的。在这项工作中，我们提出了变分推理的非线性动力学（VIND），变分推理框架，能够揭示非线性，平滑的潜在动态序列数据。该框架是PfLDS的直接扩展;包括描述空间相关线性动力学的结构化近似后验，以及依赖于定点迭代方法以实现收敛的算法。我们将VIND应用于电生理学、单细胞电压和宽场成像数据集，其重建误差具有最先进的结果。在单电池电压数据中，VIND发现了一个5D潜在空间，其变量类似于Hodgkin-Huxley模型的变量。VIND学习动态的质量通过使用它来预测未来的神经活动而进一步量化。VIND在这项任务中表现出色，在某些情况下大大优于当前的方法。
Latent variable models have been widely applied for the analysis and visualization of time series that result from techniques in experimental neuroscience. These are datasets in which the evolution of the observations is relatively smooth and possibly nonlinear. In this work we present Variational Inference for Nonlinear Dynamics (VIND), a variational inference framework that is able to uncover nonlinear, smooth latent dynamics from sequential data. The framework is a direct extension of PfLDS; including a structured approximate posterior describing spatially-dependent linear dynamics, as well as an algorithm that re- lies on the fixed-point iteration method to achieve convergence. We apply VIND to electrophysiology, single-cell voltage and widefield imaging datasets with state-of-the-art results in reconstruction error. In single-cell voltage data, VIND finds a 5D latent space, with variables akin to those of Hodgkin-Huxley-like models. The quality of VIND’s learned dynamics is further quantified by using it to predict future neural activity. VIND excels in this task, in some cases substantially outperforming current methods.