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Umfang: 1 online resource (545 pages)

Ausgabe: 1st ed.

ISBN: 9780429675683

Serie: CRC Press/Chapman and Hall Handbooks in Mathematics Series

Inhalt: Mathematicians have skills that would enable them to use data to answer questions important to them and others, and report those answers in compelling ways. Data science combines parts of mathematics, statistics, computer science. This handbook will assist mathematicians to better understand the opportunities presented by data science

Anmerkung: Cover -- Half Title -- Series Page -- Title Page -- Copyright Page -- Contents -- Foreword -- 1. Introduction -- 1.1 Who should read this book? -- 1.2 What is data science? -- 1.3 Is data science new? -- 1.4 What can I expect from this book? -- 1.5 What will this book expect from me? -- 2. Programming with Data -- 2.1 Introduction -- 2.2 The computing environment -- 2.2.1 Hardware -- 2.2.2 The command line -- 2.2.3 Programming languages -- 2.2.4 Integrated development environments (IDEs) -- 2.2.5 Notebooks -- 2.2.6 Version control -- 2.3 Best practices -- 2.3.1 Write readable code -- 2.3.2 Don't repeat yourself -- 2.3.3 Set seeds for random processes -- 2.3.4 Profile, benchmark, and optimize judiciously -- 2.3.5 Test your code -- 2.3.6 Don't rely on black boxes -- 2.4 Data-centric coding -- 2.4.1 Obtaining data -- 2.4.1.1 Files -- 2.4.1.2 The web -- 2.4.1.3 Databases -- 2.4.1.4 Other sources and concerns -- 2.4.2 Data structures -- 2.4.3 Cleaning data -- 2.4.3.1 Missing data -- 2.4.3.2 Data values -- 2.4.3.3 Outliers -- 2.4.3.4 Other issues -- 2.4.4 Exploratory data analysis (EDA) -- 2.5 Getting help -- 2.6 Conclusion -- 3. Linear Algebra -- 3.1 Data and matrices -- 3.1.1 Data, vectors, and matrices -- 3.1.2 Term-by-document matrices -- 3.1.3 Matrix storage and manipulation issues -- 3.2 Matrix decompositions -- 3.2.1 Matrix decompositions and data science -- 3.2.2 The LU decomposition -- 3.2.2.1 Gaussian elimination -- 3.2.2.2 The matrices L and U -- 3.2.2.3 Permuting rows -- 3.2.2.4 Computational notes -- 3.2.3 The Cholesky decomposition -- 3.2.4 Least-squares curve-fitting -- 3.2.5 Recommender systems and the QR decomposition -- 3.2.5.1 A motivating example -- 3.2.5.2 The QR decomposition -- 3.2.5.3 Applications of the QR decomposition -- 3.2.6 The singular value decomposition -- 3.2.6.1 SVD in our recommender system , 3.2.6.2 Further reading on the SVD -- 3.3 Eigenvalues and eigenvectors -- 3.3.1 Eigenproblems -- 3.3.2 Finding eigenvalues -- 3.3.3 The power method -- 3.3.4 PageRank -- 3.4 Numerical computing -- 3.4.1 Floating point computing -- 3.4.2 Floating point arithmetic -- 3.4.3 Further reading -- 3.5 Projects -- 3.5.1 Creating a database -- 3.5.2 The QR decomposition and query-matching -- 3.5.3 The SVD and latent semantic indexing -- 3.5.4 Searching a web -- 4. Basic Statistics -- 4.1 Introduction -- 4.2 Exploratory data analysis and visualizations -- 4.2.1 Descriptive statistics -- 4.2.2 Sampling and bias -- 4.3 Modeling -- 4.3.1 Linear regression -- 4.3.2 Polynomial regression -- 4.3.3 Group-wise models and clustering -- 4.3.4 Probability models -- 4.3.5 Maximum likelihood estimation -- 4.4 Confidence intervals -- 4.4.1 The sampling distribution -- 4.4.2 Confidence intervals from the sampling distribution -- 4.4.3 Bootstrap resampling -- 4.5 Inference -- 4.5.1 Hypothesis testing -- 4.5.1.1 First example -- 4.5.1.2 General strategy for hypothesis testing -- 4.5.1.3 Inference to compare two populations -- 4.5.1.4 Other types of hypothesis tests -- 4.5.2 Randomization-based inference -- 4.5.3 Type I and Type II error -- 4.5.4 Power and effect size -- 4.5.5 The trouble with p-hacking -- 4.5.6 Bias and scope of inference -- 4.6 Advanced regression -- 4.6.1 Transformations -- 4.6.2 Outliers and high leverage points -- 4.6.3 Multiple regression, interaction -- 4.6.4 What to do when the regression assumptions fail -- 4.6.5 Indicator variables and ANOVA -- 4.7 The linear algebra approach to statistics -- 4.7.1 The general linear model -- 4.7.2 Ridge regression and penalized regression -- 4.7.3 Logistic regression -- 4.7.4 The generalized linear model -- 4.7.5 Categorical data analysis -- 4.8 Causality -- 4.8.1 Experimental design -- 4.8.2 Quasi-experiments , 4.9 Bayesian statistics -- 4.9.1 Bayes' formula -- 4.9.2 Prior and posterior distributions -- 4.10 A word on curricula -- 4.10.1 Data wrangling -- 4.10.2 Cleaning data -- 4.11 Conclusion -- 4.12 Sample projects -- 5. Clustering -- 5.1 Introduction -- 5.1.1 What is clustering? -- 5.1.2 Example applications -- 5.1.3 Clustering observations -- 5.2 Visualization -- 5.3 Distances -- 5.4 Partitioning and the -- 5.4.1 The k-means algorithm -- 5.4.2 Issues with k-means -- 5.4.3 Example with wine data -- 5.4.4 Validation -- 5.4.5 Other partitioning algorithms -- 5.5 Hierarchical clustering -- 5.5.1 Linkages -- 5.5.2 Algorithm -- 5.5.3 Hierarchical simple example -- 5.5.4 Dendrograms and wine example -- 5.5.5 Other hierarchical algorithms -- 5.6 Case study -- 5.6.1 k-means results -- 5.6.2 Hierarchical results -- 5.6.3 Case study conclusions -- 5.7 Model-based methods -- 5.7.1 Model development -- 5.7.2 Model estimation -- 5.7.3 mclust and model selection -- 5.7.4 Example with wine data -- 5.7.5 Model-based versus k-means -- 5.8 Density-based methods -- 5.8.1 Example with iris data -- 5.9 Dealing with network data -- 5.9.1 Network clustering example -- 5.10 Challenges -- 5.10.1 Feature selection -- 5.10.2 Hierarchical clusters -- 5.10.3 Overlapping clusters, or fuzzy clustering -- 5.11 Exercises -- 6. Operations Research -- 6.1 History and background -- 6.1.1 How does OR connect to data science? -- 6.1.2 The OR process -- 6.1.3 Balance between efficiency and complexity -- 6.2 Optimization -- 6.2.1 Complexity-tractability trade-off -- 6.2.2 Linear optimization -- 6.2.2.1 Duality and optimality conditions -- 6.2.2.2 Extension to integer programming -- 6.2.3 Convex optimization -- 6.2.3.1 Duality and optimality conditions -- 6.2.4 Non-convex optimization -- 6.3 Simulation -- 6.3.1 Probability principles of simulation -- 6.3.2 Generating random variables , 6.3.2.1 Simulation from a known distribution -- 6.3.2.2 Simulation from an empirical distribution: bootstrapping -- 6.3.2.3 Markov Chain Monte Carlo (MCMC) methods -- 6.3.3 Simulation techniques for statistical and machine learning model assessment -- 6.3.3.1 Bootstrapping confidence intervals -- 6.3.3.2 Cross-validation -- 6.3.4 Simulation techniques for prescriptive analytics -- 6.3.4.1 Discrete-event simulation -- 6.3.4.2 Agent-based modeling -- 6.3.4.3 Using these tools for prescriptive analytics -- 6.4 Stochastic optimization -- 6.4.1 Dynamic programming formulation -- 6.4.2 Solution techniques -- 6.5 Putting the methods to use: prescriptive analytics -- 6.5.1 Bike-sharing systems -- 6.5.2 A customer choice model for online retail -- 6.5.3 HIV treatment and prevention -- 6.6 Tools -- 6.6.1 Optimization solvers -- 6.6.2 Simulation software and packages -- 6.6.3 Stochastic optimization software and packages -- 6.7 Looking to the future -- 6.8 Projects -- 6.8.1 The vehicle routing problem -- 6.8.2 The unit commitment problem for power systems -- 6.8.3 Modeling project -- 6.8.4 Data project -- 7. Dimensionality Reduction -- 7.1 Introduction -- 7.2 The geometry of data and dimension -- 7.3 Principal Component Analysis -- 7.3.1 Derivation and properties -- 7.3.2 Connection to SVD -- 7.3.3 How PCA is used for dimension estimation and data reduction -- 7.3.4 Topological dimension -- 7.3.5 Multidimensional scaling -- 7.4 Good projections -- 7.5 Non-integer dimensions -- 7.5.1 Background on dynamical systems -- 7.5.2 Fractal dimension -- 7.5.3 The correlation dimension -- 7.5.4 Correlation dimension of the Lorenz attractor -- 7.6 Dimension reduction on the Grassmannian -- 7.7 Dimensionality reduction in the presence of symme-try -- 7.8 Category theory applied to data visualization -- 7.9 Other methods -- 7.9.1 Nonlinear Principal Component Analysis , 7.9.2 Whitney's reduction network -- 7.9.3 The generalized singular value decomposition -- 7.9.4 False nearest neighbors -- 7.9.5 Additional methods -- 7.10 Interesting theorems on dimension -- 7.10.1 Whitney's theorem -- 7.10.2 Takens' theorem -- 7.10.3 Nash embedding theorems -- 7.10.4 Johnson-Lindenstrauss lemma -- 7.11 Conclusions -- 7.11.1 Summary and method of application -- 7.11.2 Suggested exercises -- 8. Machine Learning -- 8.1 Introduction -- 8.1.1 Core concepts of supervised learning -- 8.1.2 Types of supervised learning -- 8.2 Training dataset and test dataset -- 8.2.1 Constraints -- 8.2.2 Methods for data separation -- 8.3 Machine learning workflow -- 8.3.1 Step 1: obtaining the initial dataset -- 8.3.2 Step 2: preprocessing -- 8.3.2.1 Missing values and outliers -- 8.3.2.2 Feature engineering -- 8.3.3 Step 3: creating training and test datasets -- 8.3.4 Step 4: model creation -- 8.3.4.1 Scaling and normalization -- 8.3.4.2 Feature selection -- 8.3.5 Step 5: prediction and evaluation -- 8.3.6 Iterative model building -- 8.4 Implementing the ML workflow -- 8.4.1 Using scikit-learn -- 8.4.2 Transformer objects -- 8.5 Gradient descent -- 8.5.1 Loss functions -- 8.5.2 A powerful optimization tool -- 8.5.3 Application to regression -- 8.5.4 Support for regularization -- 8.6 Logistic regression -- 8.6.1 Logistic regression framework -- 8.6.2 Parameter estimation for logistic regression -- 8.6.3 Evaluating the performance of a classifier -- 8.7 Naïve Bayes classifier -- 8.7.1 Using Bayes' rule -- 8.7.1.1 Estimating the probabilities -- 8.7.1.2 Laplace smoothing -- 8.7.2 Health care example -- 8.8 Support vector machines -- 8.8.1 Linear SVMs in the case of linear separability -- 8.8.2 Linear SVMs without linear separability -- 8.8.3 Nonlinear SVMs -- 8.9 Decision trees -- 8.9.1 Classification trees -- 8.9.2 Regression decision trees , 8.9.3 Pruning

Weitere Ausg.: Print version Carter, Nathan Data Science for Mathematicians Milton : CRC Press LLC,c2020 ISBN 9780367027056

Sprache: Englisch

Schlagwort(e): Electronic books ; Electronic books

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URL: FULL  ((OIS Credentials Required))

UID:

Umfang: 1 online resource : , illustrations (black and white)

Ausgabe: First edition.

ISBN: 9780429675683 , 0429675682 , 9780429398292 , 0429398298 , 9780429675669 , 0429675666 , 9780429675676 , 0429675674

Serie: CRC Press/Chapman and Hall Handbooks in Mathematics

Inhalt: Mathematicians have skills that, if deepened in the right ways, would enable them to use data to answer questions important to them and others, and report those answers in compelling ways. Data science combines parts of mathematics, statistics, computer science. Gaining such power and the ability to teach has reinvigorated the careers of mathematicians. This handbook will assist mathematicians to better understand the opportunities presented by data science. As it applies to the curriculum, research, and career opportunities, data science is a fast-growing field. Contributors from both academics and industry present their views on these opportunities and how to advantage them.

Anmerkung: Programming with data / Sean Raleigh -- Linear algebra / Jeffery Leader -- Basic statistics / David White -- Clustering / Amy S. Wagaman -- Operations research / Alice Paul and Susan Martonosi -- Dimensionality reduction / Sofya Chepushtanova, Elin Farnell, Eric Kehoe, Michael Kirby, and Henry Kvinge -- Machine learning / Mahesh Agarwal, Nathan Carter, and David Oury -- Deep learning / Samuel S. Watson -- Topological data analysis / Henry Adams, Johnathan Bush, Joshua Mirth.

Weitere Ausg.: Print version: Carter, Nathan. Data Science for Mathematicians. Milton : CRC Press LLC, ©2020 ISBN 9780367027056

Sprache: Englisch

Schlagwort(e): Electronic books. ; Electronic books.

DOI: 10.1201/9780429398292

URL: https://www.taylorfrancis.com/books/9780429398292

UID:

Umfang: 1 online resource (545 pages) : , illustrations

ISBN: 9780429675683 (e-book)

Weitere Ausg.: Print version: Carter, Nathan. Data science for mathematicians. Boca Raton, Florida : CRC Press LLC, c2021 ISBN 9780367027056

Sprache: Englisch

Schlagwort(e): Electronic books.

URL: Click to View

UID:

Umfang: xv, 528 Seiten , Illustrationen, Diagramme

ISBN: 9780367027056 , 9780367528492

Serie: CRC Press/Chapman and Hall handbooks in mathematics series

Inhalt: "Mathematicians have skills that, if deepened in the right ways, would enable them to use data to answer questions important to them and others, and report those answers in compelling ways. Data science combines parts of mathematics, statistics, computer science. Gaining such power and the ability to teach has reinvigorated the careers of mathematicians. This handbook will assist mathematicians to better understand the opportunities presented by data science"--

Anmerkung: Literaturverzeichnis: Seite 475-514 , Programming with data / Sean Raleigh -- Linear algebra / Jeffery Leader -- Basic statistics / David White -- Clustering / Amy S. Wagaman -- Operations research / Alice Paul and Susan Martonosi -- Dimensionality reduction / Sofya Chepushtanova, Elin Farnell, Eric Kehoe, Michael Kirby, and Henry Kvinge -- Machine learning / Mahesh Agarwal, Nathan Carter, and David Oury -- Deep learning / Samuel S. Watson -- Topological data analysis / Henry Adams, Johnathan Bush, Joshua Mirth.

Weitere Ausg.: ISBN 9780429398292

Weitere Ausg.: Erscheint auch als Online-Ausgabe Carter, Nathan Data Science for Mathematicians Milton : CRC Press LLC, 2020 ISBN 9780429675683

Weitere Ausg.: Erscheint auch als Online-Ausgabe Data science for mathematicians Boca Raton : CRC Press, Taylor & Francis Group, 2021 ISBN 9780429398292

Weitere Ausg.: ISBN 0429398298

Weitere Ausg.: ISBN 9780429675683

Weitere Ausg.: ISBN 0429675682

Weitere Ausg.: ISBN 9780429675669

Weitere Ausg.: ISBN 0429675666

Weitere Ausg.: ISBN 9780429675676

Weitere Ausg.: ISBN 0429675674

Weitere Ausg.: Erscheint auch als Online-Ausgabe Data science for mathematicians Boca Raton : Chapman & Hall/CRC, 2020 ISBN 9780429398292

Weitere Ausg.: ISBN 9780429675669

Weitere Ausg.: ISBN 9780429675676

Weitere Ausg.: ISBN 9780429675683

Sprache: Englisch

Fachgebiete: Mathematik

Schlagwort(e): Big Data ; Datenanalyse ; Datenanalyse ; Mathematik

URL: Inhaltsverzeichnis

URL: https://www.routledge.com/Data-Science-for-Mathematicians/Carter/p/book/9780367027056

URL: Review