一种基于经验贝叶斯的高效灵活的尖峰列车模型

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摘要翻译：
精确的神经棘波反应统计模型可以表征神经群体所携带的信息。但是在记录过程中，有限的尖峰计数样本通常会导致模型过拟合。此外，目前的模型假设突触数是泊松分布的，这忽略了许多神经元表现出过度分散的突触行为这一事实。虽然负二项广义线性模型（NB-GLM）提供了一个强大的工具来建模过度分散的尖峰计数，但基于最大似然的标准NB-GLM导致了高度可变和不准确的参数估计。因此，我们提出了一种分层参数经验贝叶斯方法来估计神经元群体中的神经尖峰反应。该方法综合了广义线性模型(GLMs)和经验贝叶斯理论，旨在（1）与基于极大似然的NB-GLM和Poisson-GLM方法相比，提高参数估计的准确性和可靠性；（2）从模拟数据和实验数据中有效地捕捉到尖峰计数的过弥散性质；和（3）提供对神经相互作用和神经元群体的尖峰行为的洞察力。我们应用我们的方法研究模拟数据和实验神经数据。对仿真数据的估计表明，新框架能够准确地预测不同模型的平均峰值计数，并恢复神经群体之间的连通性权重。基于视网膜神经元的估计结果表明，该方法在保留数据的对数似然预测方面优于NB-GLM和Poisson-GLM。代码见https://doi.org/10.5281/zenodo.4704423
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英文标题：
《An Efficient and Flexible Spike Train Model via Empirical Bayes》
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作者：
Qi She, Xiaoli Wu, Beth Jelfs, Adam S. Charles, Rosa H.M.Chan
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最新提交年份：
2021
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分类信息：

一级分类：Quantitative Biology        数量生物学
二级分类：Quantitative Methods        定量方法
分类描述：All experimental, numerical, statistical and mathematical contributions of value to biology
对生物学价值的所有实验、数值、统计和数学贡献
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一级分类：Electrical Engineering and Systems Science        电气工程与系统科学
二级分类：Signal Processing        信号处理
分类描述：Theory, algorithms, performance analysis and applications of signal and data analysis, including physical modeling, processing, detection and parameter estimation, learning, mining, retrieval, and information extraction. The term "signal" includes speech, audio, sonar, radar, geophysical, physiological, (bio-) medical, image, video, and multimodal natural and man-made signals, including communication signals and data. Topics of interest include: statistical signal processing, spectral estimation and system identification; filter design, adaptive filtering / stochastic learning; (compressive) sampling, sensing, and transform-domain methods including fast algorithms; signal processing for machine learning and machine learning for signal processing applications; in-network and graph signal processing; convex and nonconvex optimization methods for signal processing applications; radar, sonar, and sensor array beamforming and direction finding; communications signal processing; low power, multi-core and system-on-chip signal processing; sensing, communication, analysis and optimization for cyber-physical systems such as power grids and the Internet of Things.
信号和数据分析的理论、算法、性能分析和应用，包括物理建模、处理、检测和参数估计、学习、挖掘、检索和信息提取。“信号”一词包括语音、音频、声纳、雷达、地球物理、生理、（生物）医学、图像、视频和多模态自然和人为信号，包括通信信号和数据。感兴趣的主题包括：统计信号处理、谱估计和系统辨识；滤波器设计；自适应滤波/随机学习；（压缩）采样、传感和变换域方法，包括快速算法；用于机器学习的信号处理和用于信号处理应用的机器学习；网络与图形信号处理；信号处理中的凸和非凸优化方法；雷达、声纳和传感器阵列波束形成和测向；通信信号处理；低功耗、多核、片上系统信号处理；信息物理系统的传感、通信、分析和优化，如电网和物联网。
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一级分类：Quantitative Biology        数量生物学
二级分类：Neurons and Cognition        神经元与认知
分类描述：Synapse, cortex, neuronal dynamics, neural network, sensorimotor control, behavior, attention
突触，皮层，神经元动力学，神经网络，感觉运动控制，行为，注意
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一级分类：Statistics        统计学
二级分类：Machine Learning        机器学习
分类描述：Covers machine learning papers (supervised, unsupervised, semi-supervised learning, graphical models, reinforcement learning, bandits, high dimensional inference, etc.) with a statistical or theoretical grounding
覆盖机器学习论文（监督，无监督，半监督学习，图形模型，强化学习，强盗，高维推理等）与统计或理论基础
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英文摘要：
  Accurate statistical models of neural spike responses can characterize the information carried by neural populations. But the limited samples of spike counts during recording usually result in model overfitting. Besides, current models assume spike counts to be Poisson-distributed, which ignores the fact that many neurons demonstrate over-dispersed spiking behaviour. Although the Negative Binomial Generalized Linear Model (NB-GLM) provides a powerful tool for modeling over-dispersed spike counts, the maximum likelihood-based standard NB-GLM leads to highly variable and inaccurate parameter estimates. Thus, we propose a hierarchical parametric empirical Bayes method to estimate the neural spike responses among neuronal population. Our method integrates both Generalized Linear Models (GLMs) and empirical Bayes theory, which aims to (1) improve the accuracy and reliability of parameter estimation, compared to the maximum likelihood-based method for NB-GLM and Poisson-GLM; (2) effectively capture the over-dispersion nature of spike counts from both simulated data and experimental data; and (3) provide insight into both neural interactions and spiking behaviours of the neuronal populations. We apply our approach to study both simulated data and experimental neural data. The estimation of simulation data indicates that the new framework can accurately predict mean spike counts simulated from different models and recover the connectivity weights among neural populations. The estimation based on retinal neurons demonstrate the proposed method outperforms both NB-GLM and Poisson-GLM in terms of the predictive log-likelihood of held-out data. Codes are available in https://doi.org/10.5281/zenodo.4704423
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PDF链接：
https://arxiv.org/pdf/1605.02869

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关键词：贝叶斯 Applications Experimental Quantitative Optimization 模型 方法 神经元 over likelihood