动态时空阵列模型的稀疏网络估计
Sparse Network Estimation for Dynamical Spatio-temporal Array Models
摘要：
神经场模型通过突触权重函数表示群体水平上的神经元通信。使用电压敏感染料（VSD）成像，可以获得具有相对高的空间和时间分辨率的神经场的测量。突触权重函数表示大脑中的功能连接，并产生时空依赖结构。我们提出了一个随机泛函微分方程建模神经领域，这导致了一个向量自回归模型的数据，通过基础扩展的突触权重函数和时间和空间离散化。将模型拟合到数据是一个实际的挑战，因为这代表了一个大规模的回归问题。通过结合局部基函数使用1-范数惩罚，可以学习大脑功能连接的稀疏网络表示，但仍然，设计矩阵的显式构造在计算上可能是禁止的。我们证明，通过使用张量积基展开，计算的惩罚估计通过一个近似梯度算法变得可行。对于计算来说，数据被组织在一个数组中是至关重要的，就像三维VSD成像数据的情况一样。这允许使用数组算法，这是内存和时间效率。所提出的方法是实现和展示在R包发电机可从CRAN。
英文摘要：
Neural field models represent neuronal communication on a population level via synaptic weight functions. Using voltage sensitive dye (VSD) imaging it is possible to obtain measurements of neural fields with a relatively high spatial and temporal resolution. The synaptic weight functions represent functional connectivity in the brain and give rise to a spatio-temporal dependence structure. We present a stochastic functional differential equation for modeling neural fields, which leads to a vector autoregressive model of the data via basis expansions of the synaptic weight functions and time and space discretization. Fitting the model to data is a pratical challenge as this represents a large scale regression problem. By using a 1-norm penalty in combination with localized basis functions it is possible to learn a sparse network representation of the functional connectivity of the brain, but still, the explicit construction of a design matrix can be computationally prohibitive. We demonstrate that by using tensor product basis expansions, the computation of the penalized estimator via a proximal gradient algorithm becomes feasible. It is crucial for the computations that the data is organized in an array as is the case for the three dimensional VSD imaging data. This allows for the use of array arithmetic that is both memory and time efficient.The proposed method is implemented and showcased in the R package dynamo available from CRAN.
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