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Identification of sparse neural functional connectivity using penalized likelihood estimation and basis functions

机译:使用惩罚似然估计和基函数识别稀疏神经功能连接

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摘要

One key problem in computational neuroscience and neural engineering is the identification and modeling of functional connectivity in the brain using spike train data. To reduce model complexity, alleviate overfitting, and thus facilitate model interpretation, sparse representation and estimation of functional connectivity is needed. Sparsities include global sparsity, which captures the sparse connectivities between neurons, and local sparsity, which reflects the active temporal ranges of the input-output dynamical interactions. In this paper, we formulate a generalized functional additive model (GFAM) and develop the associated penalized likelihood estimation methods for such a modeling problem. A GFAM consists of a set of basis functions convolving the input signals, and a link function generating the firing probability of the output neuron from the summation of the convolutions weighted by the sought model coefficients. Model sparsities are achieved by using various penalized likelihood estimations and basis functions. Specifically, we introduce two variations of the GFAM using a global basis (e.g., Laguerre basis) and group LASSO estimation, and a local basis (e.g., B-spline basis) and group bridge estimation, respectively. We further develop an optimization method based on quadratic approximation of the likelihood function for the estimation of these models. Simulation and experimental results show that both group-LASSO-Laguerre and group-bridge-B-spline can capture faithfully the global sparsities, while the latter can replicate accurately and simultaneously both global and local sparsities. The sparse models outperform the full models estimated with the standard maximum likelihood method in out-of-sample predictions.
机译:计算神经科学和神经工程学中的一个关键问题是使用峰值训练数据识别和建模大脑中的功能连接。为了减少模型的复杂性,减轻过度拟合,从而促进模型的解释,需要稀疏表示和功能连接的估计。稀疏性包括全局稀疏性和局部稀疏性,全局稀疏性捕获了神经元之间的稀疏连接性,而局部稀疏性反映了输入输出动态交互的活动时间范围。在本文中,我们制定了广义功能加性模型(GFAM),并针对此类建模问题开发了相关的惩罚似然估计方法。 GFAM包括一组对输入信号进行卷积的基函数,以及一个链接函数,该链接函数根据由所寻找模型系​​数加权的卷积之和生成输出神经元的触发概率。模型稀疏度是通过使用各种惩罚性似然估计和基函数来实现的。具体而言,我们分别使用全局基础(例如Laguerre基础)和组LASSO估计以及局部基础(例如B样条基础)和组桥估计来介绍GFAM的两种变体。我们进一步开发了一种基于似然函数二次逼近的优化方法,用于估算这些模型。仿真和实验结果表明,LASSO-Laguerre组和B桥-B组样条曲线都可以忠实地捕获全局稀疏度,而后者可以准确并同时复制全局稀疏度和局部稀疏度。在样本外预测中,稀疏模型的性能优于使用标准最大似然法估计的完整模型。

著录项

  • 来源
    《Journal of Computational Neuroscience》 |2013年第3期|335-357|共23页
  • 作者单位

    Department of Biomedical Engineering, University of Southern California, 403 Hedco Neuroscience Building,Los Angeles, CA 90089, USA,Center for Neural Engineering, University of Southern California,Los Angeles, CA 90089, USA;

    Department of Statistics, Colorado State University,Fort Collins, CO 80523, USA;

    Department of Statistics, Colorado State University,Fort Collins, CO 80523, USA;

    Department of Biomedical Engineering, University of Southern California, 403 Hedco Neuroscience Building,Los Angeles, CA 90089, USA,Center for Neural Engineering, University of Southern California,Los Angeles, CA 90089, USA;

    Department of Physiology & Pharmacology,Wake Forest University, School of Medicine,Winston-Salem, NC 27157, USA;

    Department of Physiology & Pharmacology,Wake Forest University, School of Medicine,Winston-Salem, NC 27157, USA;

    Department of Biomedical Engineering, University of Southern California, 403 Hedco Neuroscience Building,Los Angeles, CA 90089, USA,Center for Neural Engineering, University of Southern California,Los Angeles, CA 90089, USA,Program in Neuroscience, University of Southern California,Los Angeles, CA 90089, USA;

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  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    Functional connectivity; Generalized linear model; Sparsity; Penalized likelihood; Basis function; Spike trains; Temporal coding;

    机译:功能连接;广义线性模型;稀疏性受罚的可能性;基函数;尖刺火车;时间编码;

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