Pakman Ari, Huggins Jonathan, Smith Carl, Paninski Liam
J Comput Neurosci. 2014 Jun;36(3):415-43. doi: 10.1007/s10827-013-0478-0.
We present fast methods for filtering voltage measurements and performing optimal inference of the location and strength of synaptic connections in large dendritic trees. Given noisy, subsampled voltage observations we develop fast l1-penalized regression methods for Kalman state-space models of the neuron voltage dynamics. The value of the l1-penalty parameter is chosen using cross-validation or, for low signal-to-noise ratio, a Mallows' Cp-like criterion. Using low-rank approximations, we reduce the inference runtime from cubic to linear in the number of dendritic compartments. We also present an alternative, fully Bayesian approach to the inference problem using a spike-and-slab prior. We illustrate our results with simulations on toy and real neuronal geometries. We consider observation schemes that either scan the dendritic geometry uniformly or measure linear combinations of voltages across several locations with random coefficients. For the latter, we show how to choose the coefficients to offset the correlation between successive measurements imposed by the neuron dynamics. This results in a "compressed sensing" observation scheme, with an important reduction in the number of measurements required to infer the synaptic weights.
我们提出了用于过滤电压测量值以及对大型树突状树突中突触连接的位置和强度进行最优推断的快速方法。给定有噪声的、下采样的电压观测值，我们为神经元电压动力学的卡尔曼状态空间模型开发了快速的 l1 惩罚回归方法。l1 惩罚参数的值使用交叉验证来选择，或者对于低信噪比的情况，使用类似 Mallows' Cp 的准则来选择。通过使用低秩近似，我们将推断运行时间从与树突状隔室数量的立方关系减少到线性关系。我们还提出了一种使用尖峰和平板先验的替代的、完全贝叶斯方法来解决推断问题。我们通过在玩具和真实神经元几何结构上的模拟来说明我们的结果。我们考虑了两种观测方案，一种是均匀扫描树突状几何结构，另一种是测量具有随机系数的多个位置的电压线性组合。对于后者，我们展示了如何选择系数以抵消由神经元动力学引起的连续测量之间的相关性。这导致了一种“压缩感知”观测方案，在推断突触权重所需的测量数量方面有重要减少。
