數據科學中的數學方法 (英文版) 任景莉王海燕 9787030747563 【台灣高等教育出版社】

Name: 數據科學中的數學方法 (英文版) 任景莉 王海燕 9787030747563 【台灣高等教育出版社】
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書名：數據科學中的數學方法 (英文版)
ISBN：9787030747563
出版社：科學
著編譯者：任景莉王海燕
叢書名：信息與計算科學叢書
頁數：246
所在地：中國大陸 *此為代購商品
書號：1544183
可大量預訂，請先連絡。

內容簡介

數據科學是建立在數學之上的。在本書中，我們將涵蓋數據科學中廣泛使用的數學工具，包括微積分、線性代數、優化、網路分析、概率和微分方程。特別地，本書介紹了一種基於網路分析的新方法，將大數據集成到常微分方程和偏微分方程的框架中進行數據分析和預測。本書中，我們把數學與數據科學中出現的示例和問題相結合，並展示高等數學，特別是數據驅動的微分方程在數據科學中的應用。

Preface
Acknowledgments
1 Linear algebra
1 1 Introduction
1 2 Elements of linear algebra
1 2 1 Linear spaces
1 2 2 Orthogonality
1 2 3 Gram-Schmidt process
1 2 4 Eigenvalues and eigenvectors
1 3 Linear regression
1 3 1 QR decomposition
1 3 2 Least-squares problems
1 3 3 Linear regression
1 4 Principal component analysis
1 4 1 Singular value decomposition
1 4 2 Low-rank matrix approximations
1 4 3 Principal component analysis
2 Probability
2 1 Introduction
2 2 Probability distribution
2 2 1 Probability axioms
2 2 2 Conditional probability
2 2 3 Discrete random variables
2 2 4 Continues random variables
2 3 Independent variables and random samples
2 3 1 Joint probability distributions
2 3 2 Correlation and dependence
2 3 3 Random samples
2 4 Maximum likelihood estimation
2 4 1 MLE for random samples
2 4 2 Linear regression
3 Calculus and optimization
3 1 Introduction
3 2 Continuity and differentiation
3 2 1 Limits and continuity
3 2 2 Derivatives
3 2 3 Taylor's theorem
3 3 Unconstrained optimization
3 3 1 Necessary and sufficient conditions of local minimizers
3 3 2 Convexity and global minimizers
3 3 3 Gradient descent
3 4 Logistic regression
3 5 K-means
3 6 Support vector machine
3 7 Neural networks
3 7 1 Mathematical formulation
3 7 2 Activation functions
3 7 3 Cost function
3 7 4 Backpropagation
3 7 5 Backpropagation algorithm
4 Network analysis
4 1 Introduction
4 2 Graph modeling
4 3 Spectral graph bipartitioning
4 4 Network embedding
4 5 Network based influenza prediction
4 5 1 Introduction
4 5 2 Data analysis with spatial networks
4 5 3 ANN method for prediction
5 Ordinary differential equations
5 1 Introduction
5 2 Basic differential equation models
5 2 1 Logistic differential equations
5 2 2 Epidemical model
5 3 Prediction of daily PM2 5 concentration
5 3 1 Introduction
5 3 2 Genetic programming for ODE
5 3 3 Experimental results and prediction analysis
5 4 Analysis of COVID-19
5 4 1 Introduction
5 4 2 Modeling and parameter estimation
5 4 3 Model simulations
5 4 4 Conclusion and perspective
5 5 Analysis of COVD-19 in Arizona
5 5 1 Introduction
5 5 2 Data sources and collection
5 5 3 Model simulations
5 5 4 Rermarks
6 Partial differential equations
6 1 Introduction
6 2 Formulation of partial differential equation models
6 3 Bitcoin price prediction
6 3 1 Network analysis for bitcoin
6 3 2 PDE modeling
6 3 3 Bitcoin price prediction
6 3 4 Remarks
6 4 Prediction of PM2 5 In China
6 4 1 Introduction
6 4 2 PDE model for PM2 5
6 4 3 Data collection and clustering
6 4 4 PM2 5 prediction
6 4 5 Remarks
6 5 Prediction of COVD-19 in Arizona
6 5 1 Introduction
6 5 2 Arizona COVD data
6 5 3 PDE modeling of Arizona COVID-19
6 5 4 Model prediction
6 5 5 Remarks
6 6 Compliance with COVID-19 mitigation policies in the US
6 6 1 Introduction
6 6 2 Data set sources and collection
6 6 3 PDE model for quantlfying compliance with COVID-19 policies
6 6 4 Model prediction
6 6 5 Analysis of compliance with the US COVID-19 mitigation policy
6 6 6 Remarks
Bibllography
Index
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