دانلود کتاب Data science for mathematicians

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Cover......Page 1
Half Title......Page 2
Series Page......Page 3
Title Page......Page 4
Copyright Page......Page 5
Contents......Page 6
Foreword......Page 16
1.1 Who should read this book?......Page 18
1.2 What is data science?......Page 20
1.3 Is data science new?......Page 23
1.4 What can I expect from this book?......Page 25
1.5 What will this book expect from me?......Page 27
2. Programming with Data......Page 30
2.2.1 Hardware......Page 31
2.2.2 The command line......Page 32
2.2.3 Programming languages......Page 33
2.2.4 Integrated development environments (IDEs)......Page 34
2.2.5 Notebooks......Page 35
2.2.6 Version control......Page 39
2.3.1 Write readable code......Page 40
2.3.2 Don\'t repeat yourself......Page 43
2.3.4 Profile, benchmark, and optimize judiciously......Page 44
2.3.5 Test your code......Page 45
2.3.6 Don\'t rely on black boxes......Page 46
2.4.1.1 Files......Page 47
2.4.1.3 Databases......Page 48
2.4.1.4 Other sources and concerns......Page 50
2.4.2 Data structures......Page 51
2.4.3 Cleaning data......Page 52
2.4.3.1 Missing data......Page 53
2.4.3.2 Data values......Page 54
2.4.3.4 Other issues......Page 55
2.4.4 Exploratory data analysis (EDA)......Page 57
2.6 Conclusion......Page 58
3. Linear Algebra......Page 60
3.1.1 Data, vectors, and matrices......Page 61
3.1.2 Term-by-document matrices......Page 63
3.1.3 Matrix storage and manipulation issues......Page 64
3.2.2.1 Gaussian elimination......Page 68
3.2.2.2 The matrices L and U......Page 70
3.2.2.3 Permuting rows......Page 72
3.2.2.4 Computational notes......Page 73
3.2.3 The Cholesky decomposition......Page 75
3.2.4 Least-squares curve-fitting......Page 77
3.2.5.1 A motivating example......Page 80
3.2.5.2 The QR decomposition......Page 82
3.2.5.3 Applications of the QR decomposition......Page 87
3.2.6 The singular value decomposition......Page 88
3.2.6.1 SVD in our recommender system......Page 91
3.2.6.2 Further reading on the SVD......Page 94
3.3.1 Eigenproblems......Page 95
3.3.2 Finding eigenvalues......Page 99
3.3.3 The power method......Page 101
3.3.4 PageRank......Page 103
3.4.2 Floating point arithmetic......Page 109
3.4.3 Further reading......Page 111
3.5.1 Creating a database......Page 112
3.5.4 Searching a web......Page 113
4. Basic Statistics......Page 116
4.1 Introduction......Page 117
4.2 Exploratory data analysis and visualizations......Page 120
4.2.1 Descriptive statistics......Page 123
4.2.2 Sampling and bias......Page 126
4.3 Modeling......Page 128
4.3.1 Linear regression......Page 129
4.3.2 Polynomial regression......Page 133
4.3.3 Group-wise models and clustering......Page 134
4.3.4 Probability models......Page 135
4.3.5 Maximum likelihood estimation......Page 139
4.4 Confidence intervals......Page 141
4.4.1 The sampling distribution......Page 142
4.4.2 Confidence intervals from the sampling distribution......Page 144
4.4.3 Bootstrap resampling......Page 147
4.5.1.1 First example......Page 150
4.5.1.2 General strategy for hypothesis testing......Page 153
4.5.1.3 Inference to compare two populations......Page 154
4.5.1.4 Other types of hypothesis tests......Page 155
4.5.2 Randomization-based inference......Page 156
4.5.4 Power and effect size......Page 159
4.5.5 The trouble with p-hacking......Page 160
4.5.6 Bias and scope of inference......Page 161
4.6.1 Transformations......Page 162
4.6.2 Outliers and high leverage points......Page 163
4.6.3 Multiple regression, interaction......Page 165
4.6.4 What to do when the regression assumptions fail......Page 169
4.6.5 Indicator variables and ANOVA......Page 172
4.7 The linear algebra approach to statistics......Page 176
4.7.1 The general linear model......Page 177
4.7.2 Ridge regression and penalized regression......Page 182
4.7.3 Logistic regression......Page 183
4.7.4 The generalized linear model......Page 188
4.7.5 Categorical data analysis......Page 189
4.8.1 Experimental design......Page 190
4.8.2 Quasi-experiments......Page 193
4.9.1 Bayes\' formula......Page 194
4.9.2 Prior and posterior distributions......Page 195
4.10.1 Data wrangling......Page 197
4.10.2 Cleaning data......Page 198
4.12 Sample projects......Page 199
5. Clustering......Page 202
5.1.2 Example applications......Page 203
5.1.3 Clustering observations......Page 204
5.2 Visualization......Page 205
5.3 Distances......Page 206
5.4.1 The k-means algorithm......Page 210
5.4.2 Issues with k-means......Page 212
5.4.3 Example with wine data......Page 214
5.4.4 Validation......Page 217
5.5 Hierarchical clustering......Page 221
5.5.1 Linkages......Page 222
5.5.2 Algorithm......Page 223
5.5.3 Hierarchical simple example......Page 224
5.5.4 Dendrograms and wine example......Page 225
5.6 Case study......Page 228
5.6.1 k-means results......Page 229
5.6.2 Hierarchical results......Page 231
5.6.3 Case study conclusions......Page 232
5.7.1 Model development......Page 234
5.7.2 Model estimation......Page 235
5.7.4 Example with wine data......Page 237
5.7.5 Model-based versus k-means......Page 238
5.8 Density-based methods......Page 241
5.8.1 Example with iris data......Page 243
5.9 Dealing with network data......Page 245
5.9.1 Network clustering example......Page 246
5.10.1 Feature selection......Page 249
5.10.2 Hierarchical clusters......Page 250
5.11 Exercises......Page 251
6. Operations Research......Page 256
6.1.1 How does OR connect to data science?......Page 258
6.1.2 The OR process......Page 259
6.1.3 Balance between efficiency and complexity......Page 260
6.2 Optimization......Page 261
6.2.1 Complexity-tractability trade-off......Page 263
6.2.2 Linear optimization......Page 264
6.2.2.1 Duality and optimality conditions......Page 266
6.2.3 Convex optimization......Page 269
6.2.3.1 Duality and optimality conditions......Page 273
6.2.4 Non-convex optimization......Page 275
6.3 Simulation......Page 277
6.3.1 Probability principles of simulation......Page 278
6.3.2.1 Simulation from a known distribution......Page 279
6.3.2.3 Markov Chain Monte Carlo (MCMC) methods......Page 284
6.3.3.1 Bootstrapping confidence intervals......Page 286
6.3.3.2 Cross-validation......Page 287
6.3.4 Simulation techniques for prescriptive analytics......Page 288
6.3.4.2 Agent-based modeling......Page 289
6.4 Stochastic optimization......Page 290
6.4.1 Dynamic programming formulation......Page 291
6.4.2 Solution techniques......Page 292
6.5.1 Bike-sharing systems......Page 294
6.5.2 A customer choice model for online retail......Page 295
6.5.3 HIV treatment and prevention......Page 296
6.6 Tools......Page 297
6.6.1 Optimization solvers......Page 298
6.6.2 Simulation software and packages......Page 299
6.7 Looking to the future......Page 300
6.8.1 The vehicle routing problem......Page 302
6.8.2 The unit commitment problem for power systems......Page 303
6.8.4 Data project......Page 306
7. Dimensionality Reduction......Page 308
7.1 Introduction......Page 309
7.2 The geometry of data and dimension......Page 311
7.3.1 Derivation and properties......Page 315
7.3.3 How PCA is used for dimension estimation and data reduction......Page 317
7.3.4 Topological dimension......Page 318
7.3.5 Multidimensional scaling......Page 320
7.4 Good projections......Page 321
7.5 Non-integer dimensions......Page 323
7.5.1 Background on dynamical systems......Page 324
7.5.2 Fractal dimension......Page 325
7.5.3 The correlation dimension......Page 326
7.5.4 Correlation dimension of the Lorenz attractor......Page 328
7.6 Dimension reduction on the Grassmannian......Page 329
7.7 Dimensionality reduction in the presence of symme-try......Page 335
7.8 Category theory applied to data visualization......Page 338
7.9.1 Nonlinear Principal Component Analysis......Page 343
7.9.2 Whitney\'s reduction network......Page 347
7.9.3 The generalized singular value decomposition......Page 348
7.9.5 Additional methods......Page 349
7.10.2 Takens\' theorem......Page 350
7.10.3 Nash embedding theorems......Page 351
7.10.4 Johnson-Lindenstrauss lemma......Page 352
7.11.2 Suggested exercises......Page 353
8. Machine Learning......Page 356
8.1 Introduction......Page 357
8.1.1 Core concepts of supervised learning......Page 358
8.2.1 Constraints......Page 359
8.2.2 Methods for data separation......Page 361
8.3 Machine learning workflow......Page 363
8.3.1 Step 1: obtaining the initial dataset......Page 365
8.3.2 Step 2: preprocessing......Page 367
8.3.2.1 Missing values and outliers......Page 368
8.3.2.2 Feature engineering......Page 369
8.3.3 Step 3: creating training and test datasets......Page 370
8.3.4.1 Scaling and normalization......Page 371
8.3.4.2 Feature selection......Page 372
8.3.5 Step 5: prediction and evaluation......Page 374
8.3.6 Iterative model building......Page 375
8.4.1 Using scikit-learn......Page 377
8.4.2 Transformer objects......Page 380
8.5.1 Loss functions......Page 381
8.5.2 A powerful optimization tool......Page 382
8.5.3 Application to regression......Page 383
8.5.4 Support for regularization......Page 384
8.6 Logistic regression......Page 387
8.6.2 Parameter estimation for logistic regression......Page 388
8.6.3 Evaluating the performance of a classifier......Page 390
8.7.1 Using Bayes\' rule......Page 394
8.7.1.2 Laplace smoothing......Page 396
8.7.2 Health care example......Page 397
8.8 Support vector machines......Page 399
8.8.1 Linear SVMs in the case of linear separability......Page 400
8.8.2 Linear SVMs without linear separability......Page 403
8.8.3 Nonlinear SVMs......Page 406
8.9 Decision trees......Page 409
8.9.1 Classification trees......Page 412
8.9.2 Regression decision trees......Page 415
8.9.3 Pruning......Page 416
8.10 Ensemble methods......Page 419
8.10.2 Random forests......Page 420
8.10.3 Boosting......Page 421
8.11 Next steps......Page 423
9. Deep Learning......Page 426
9.1.1 Overview......Page 427
9.1.2 History of neural networks......Page 428
9.2 Multilayer perceptrons......Page 430
9.2.1 Backpropagation......Page 431
9.2.3 Neural networks for classification......Page 434
9.3 Training techniques......Page 435
9.3.2 Optimization algorithms......Page 436
9.3.5 Weight regularization......Page 438
9.4 Convolutional neural networks......Page 439
9.4.1 Convnet layers......Page 440
9.4.2 Convolutional architectures for ImageNet......Page 441
9.5 Recurrent neural networks......Page 446
9.5.1 LSTM cells......Page 447
9.6.1 Overview......Page 448
9.6.2 Attention layers......Page 449
9.6.5 Using transformers......Page 451
9.7.1 Hardware acceleration......Page 452
9.7.2 History of deep learning frameworks......Page 453
9.7.3 TensorFlow with Keras......Page 455
9.9 Exercises and solutions......Page 457
10.1 Introduction......Page 458
10.2.2 Molecule configurations......Page 460
10.2.4 Dynamical systems......Page 462
10.3 Topology......Page 463
10.4 Simplicial complexes......Page 464
10.5 Homology......Page 466
10.5.1 Simplicial homology......Page 467
10.5.2 Homology definitions......Page 468
10.5.3 Homology example......Page 469
10.5.4 Homology computation using linear algebra......Page 470
10.6 Persistent homology......Page 474
10.7 Sublevelset persistence......Page 480
10.8 Software and exercises......Page 481
10.10 Appendix: stability of persistent homology......Page 484
10.10.1 Distances between datasets......Page 485
10.10.2 Bottleneck distance and visualization......Page 488
10.10.3 Stability results......Page 490
Bibliography......Page 492
Index......Page 532