神經科學資料分析
Data Analysis in Neuroscience
| 節 | 週三 |
|---|---|
3 10:10–11:00 | 神經科學資料分析 YL839 2 節連堂 |
4 11:10–12:00 |
* 根據陽明交大上課時間表所列
本課程旨在概述神經科學研究領域中常用的統計、分析和計算工具。 它將側重於以比正式方式更直觀的方式描述各種數據分析方法的強度和適用性。 通過實用、簡化的練習,它旨在為學生提供可能對他們未來在該領域的研究有用的工具。 This course is intended to provide an overview on the statistical, analytic, and computational tools that are commonly used in the research field of neuroscience. It will focus on characterizing the strength and applicability of various data analytical approaches in some more intuitive than formal ways. Through practical, simplified exercises, it aims to initiate students with tools that are likely to be useful for their future research in the field.
介紹神經科學數據處理中的常用計算和分析方法 To provide an introduction to common computational and analytic methods in the processing of neuroscience data
平時及期末作業 Homework and take-home final
| 週次 | 主題 |
|---|---|
| 第 1 週 | 課程介紹、統計模型、基於模型的分析、參數估計 Course introduction, Statistical models, Model-based analysis, Parameter estimation |
| 第 2 週 | 優化:梯度下降、期望最大化;假設檢驗 Optimizations: gradient descent, expectation maximization; Hypothesis testing |
| 第 3 週 | 多元線性回歸;一般線性模型;多元回歸;典型相關分析 Multiple linear regression; General linear model; Multivariate regression; Canonical correlation analysis |
| 第 4 週 | Ridge & LASSO 回歸;局部線性回歸;基礎擴展和?條;k-最近鄰法 Ridge & LASSO regression; Local linear regression; Basis expansions & splines; k-nearest neighbor method |
| 第 5 週 | 人工神經網絡和非線性回歸;判別分析;邏輯回歸 Artificial neural networks and nonlinear regression; Discriminant analysis; Logistic regression |
| 第 6 週 | 費雪判別標準;邏輯回歸;用於分類的 KNN Fisher’s discriminant criterion; Logistic regression; KNN for classification |
| 第 7 週 | 最大邊距分類器;內核函數;支持向量機 Maximum margin classifiers; Kernel functions; Support vector machines |
| 第 8 週 | 模型複雜度和選擇 Model complexity and selection |
| 第 9 週 | 高斯混合模型;密度估計;聚類:K-means 和 k-medoids Gaussian mixture models; Density estimation; Clustering: K-means and k-medoids |
| 第 10 週 | 層次聚類分析;類數確定;模式搜索 Hierarchical cluster analysis; Number of classes determination; Mode hunting |
| 第 11 週 | 主成分分析;因子分析;多維縮放;局部線性嵌入;獨立成分分析 Principal component analysis; Factor analysis; Multidimensional scaling; Locally linear embedding; Independent component analysis |
| 第 12 週 | 線性時間序列分析:自相關;功率譜;白噪聲;平穩性;遍歷性;多元模型 Linear time series analysis: Autocorrelation; Power spectrum; White noise; Stationarity; Ergodicity; Multivariate models |
| 第 13 週 | 多元AR模型;模型參數的統計推斷;計數和點過程 Multivariate AR model; Statistical inference of model parameters; Count and point process |
| 第 14 週 | 多元AR模型的實現;格蘭傑因果關係;格蘭傑因果關係的 AR 和 CCA 計算 Implementation of multivariate AR model; Granger causality; AR and CCA calculations for Granger causality |
| 第 15 週 | 具有潛在變量的線性序列:狀態空間模型;高斯過程因子分析;計數和點系列;時間序列的引導 Linear series with latent variables: State-space models; Gaussian-process factor analysis; Count and point series; Bootstrapping for time series |
| 第 16 週 | 時間序列分析中的非線性概念:檢測非線性;非參數建模;變化點分析;隱馬爾可夫模型 Nonlinear concepts in time series analysis: Detecting nonlinearity; Nonparametric modeling; Change point analysis; Hidden Markov model |
| 第 17 週 | 非線性動力系統;映射;遞歸神經網絡;微分方程;吸引子與混沌 Nonlinear dynamical systems; Maps; Recurrent neural networks; Differential equations; Attractors & chaos |
| 第 18 週 | 非線性振盪和鎖相 Nonlinear oscillations & phase-locking |
Advanced Data Analysis in Neuroscience: Integrating Statistical and Computational Models, Durstewitz, 2017. (Main) https://doi.org/10.1007/978-3-319-59976-2 https://link.springer.com/book/10.1007%2F978-3-319-59976-2