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E-raamat: Statistical Analysis Techniques in Particle Physics: Fits, Density Estimation and Supervised Learning

(MathWorks, Natick, USA), (California Institute of Technology, Pasadena, USA)
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  • Ilmumisaeg: 24-Oct-2013
  • Kirjastus: Blackwell Verlag GmbH
  • Keel: eng
  • ISBN-13: 9783527677290
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Statistical Analysis Techniques in Particle Physics: Fits, Density Estimation and Supervised LearningSuurem pilt
  • Formaat: EPUB+DRM
  • Ilmumisaeg: 24-Oct-2013
  • Kirjastus: Blackwell Verlag GmbH
  • Keel: eng
  • ISBN-13: 9783527677290
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Assuming that readers are already familiar with basic probability theory and basic methods in parameter estimation such as maximum likelihood, Narsky and Porter introduce physicists to the tools of statistics that have been developed in an environment of virtually unlimited computing power. They focus on supervised machine learning, and within it on classification rather than regression. Among the topics are parameter likelihood fits, linear transformations and dimensionality reduction, assessing classifier performance, local learning and kernel expansion, and bump hunting in multivariate data. Annotation ©2014 Book News, Inc., Portland, OR (booknews.com)

Modern analysis of HEP data needs advanced statistical tools to separate signal from background. This is the first book which focuses on machine learning techniques. It will be of interest to almost every high energy physicist, and, due to its coverage, suitable for students.
Acknowledgements xiii
Notation and Vocabulary xv
1 Why We Wrote This Book and How You Should Read It
1(4)
2 Parametric Likelihood Fits
5(34)
2.1 Preliminaries
5(7)
2.1.1 Example: CP Violation via Mixing
7(2)
2.1.2 The Exponential Family
9(1)
2.1.3 Confidence Intervals
10(1)
2.1.4 Hypothesis Tests
11(1)
2.2 Parametric Likelihood Fits
12(9)
2.2.1 Nuisance Parameters
16(1)
2.2.2 Confidence Intervals from Pivotal Quantities
17(2)
2.2.3 Asymptotic Inference
19(1)
2.2.4 Profile Likelihood
20(1)
2.2.5 Conditional Likelihood
20(1)
2.3 Fits for Small Statistics
21(5)
2.3.1 Sample Study of Coverage at Small Statistics
22(3)
2.3.2 When the pdf Goes Negative
25(1)
2.4 Results Near the Boundary of a Physical Region
26(2)
2.5 Likelihood Ratio Test for Presence of Signal
28(3)
2.6 sPlots
31(4)
2.7 Exercises
35(4)
References
37(2)
3 Goodness of Fit
39(24)
3.1 Binned Goodness of Fit Tests
41(5)
3.2 Statistics Converging to Chi-Square
46(3)
3.3 Univariate Unbinned Goodness of Fit Tests
49(3)
3.3.1 Kolmogorov--Smirnov
49(1)
3.3.2 Anderson--Darling
50(1)
3.3.3 Watson
51(1)
3.3.4 Neyman Smooth
51(1)
3.4 Multivariate Tests
52(7)
3.4.1 Energy Tests
53(1)
3.4.2 Transformations to a Uniform Distribution
54(1)
3.4.3 Local Density Tests
55(1)
3.4.4 Kernel-based Tests
56(1)
3.4.5 Mixed Sample Tests
57(1)
3.4.6 Using a Classifier
58(1)
3.5 Exercises
59(4)
References
61(2)
4 Resampling Techniques
63(26)
4.1 Permutation Sampling
63(2)
4.2 Bootstrap
65(5)
4.2.1 Bootstrap Confidence Intervals
68(2)
4.2.2 Smoothed Bootstrap
70(1)
4.2.3 Parametric Bootstrap
70(1)
4.3 Jackknife
70(6)
4.4 BCa Confidence Intervals
76(2)
4.5 Cross-Validation
78(4)
4.6 Resampling Weighted Observations
82(4)
4.7 Exercises
86(3)
References
86(3)
5 Density Estimation
89(32)
5.1 Empirical Density Estimate
90(1)
5.2 Histograms
90(2)
5.3 Kernel Estimation
92(1)
5.3.1 Multivariate Kernel Estimation
92(1)
5.4 Ideogram
93(1)
5.5 Parametric vs. Nonparametric Density Estimation
93(1)
5.6 Optimization
94(6)
5.6.1 Choosing Histogram Binning
97(3)
5.7 Estimating Errors
100(2)
5.8 The Curse of Dimensionality
102(1)
5.9 Adaptive Kernel Estimation
103(2)
5.10 Naive Bayes Classification
105(1)
5.11 Multivariate Kernel Estimation
106(2)
5.12 Estimation Using Orthogonal Series
108(3)
5.13 Using Monte Carlo Models
111(1)
5.14 Unfolding
112(8)
5.14.1 Unfolding: Regularization
116(4)
5.15 Exercises
120(1)
References
120(1)
6 Basic Concepts and Definitions of Machine Learning
121(8)
6.1 Supervised, Unsupervised, and Semi-Supervised
121(2)
6.2 Tall and Wide Data
123(1)
6.3 Batch and Online Learning
124(1)
6.4 Parallel Learning
125(2)
6.5 Classification and Regression
127(2)
References
128(1)
7 Data Preprocessing
129(16)
7.1 Categorical Variables
129(3)
7.2 Missing Values
132(7)
7.2.1 Likelihood Optimization
134(1)
7.2.2 Deletion
135(2)
7.2.3 Augmentation
137(1)
7.2.4 Imputation
137(2)
7.2.5 Other Methods
139(1)
7.3 Outliers
139(2)
7.4 Exercises
141(4)
References
142(3)
8 Linear Transformations and Dimensionality Reduction
145(20)
8.1 Centering, Scaling, Reflection and Rotation
145(1)
8.2 Rotation and Dimensionality Reduction
146(1)
8.3 Principal Component Analysis (PCA)
147(11)
8.3.1 Theory
148(1)
8.3.2 Numerical Implementation
149(1)
8.3.3 Weighted Data
150(1)
8.3.4 How Many Principal Components Are Enough?
151(3)
8.3.5 Example: Apply PCA and Choose the Optimal Number of Components
154(4)
8.4 Independent Component Analysis (ICA)
158(5)
8.4.1 Theory
158(3)
8.4.2 Numerical implementation
161(1)
8.4.3 Properties
162(1)
8.5 Exercises
163(2)
References
163(2)
9 Introduction to Classification
165(30)
9.1 Loss Functions: Hard Labels and Soft Scores
165(3)
9.2 Bias, Variance, and Noise
168(5)
9.3 Training, Validating and Testing: The Optimal Splitting Rule
173(4)
9.4 Resampling Techniques: Cross-Validation and Bootstrap
177(5)
9.4.1 Cross-Validation
177(2)
9.4.2 Bootstrap
179(2)
9.4.3 Sampling with Stratification
181(1)
9.5 Data with Unbalanced Classes
182(8)
9.5.1 Adjusting Prior Probabilities
183(1)
9.5.2 Undersampling the Majority Class
184(1)
9.5.3 Oversampling the Minority Class
185(1)
9.5.4 Example: Classification of Forest Cover Type Data
186(4)
9.6 Learning with Cost
190(1)
9.7 Exercises
191(4)
References
192(3)
10 Assessing Classifier Performance
195(26)
10.1 Classification Error and Other Measures of Predictive Power
195(1)
10.2 Receiver Operating Characteristic (ROC) and Other Curves
196(14)
10.2.1 Empirical ROC curve
196(2)
10.2.2 Other Performance Measures
198(1)
10.2.3 Optimal Operating Point
198(2)
10.2.4 Area Under Curve
200(1)
10.2.5 Smooth ROC Curves
200(5)
10.2.6 Confidence Bounds for ROC Curves
205(5)
10.3 Testing Equivalence of Two Classification Models
210(5)
10.4 Comparing Several Classifiers
215(2)
10.5 Exercises
217(4)
References
218(3)
11 Linear and Quadratic Discriminant Analysis, Logistic Regression, and Partial Least Squares Regression
221(30)
11.1 Discriminant Analysis
221(10)
11.1.1 Estimating the Covariance Matrix
223(2)
11.1.2 Verifying Discriminant Analysis Assumptions
225(1)
11.1.3 Applying LDA When LDA Assumptions Are Invalid
226(2)
11.1.4 Numerical Implementation
228(1)
11.1.5 Regularized Discriminant Analysis
228(1)
11.1.6 LDA for Variable Transformation
229(2)
11.2 Logistic Regression
231(4)
11.2.1 Binomial Logistic Regression: Theory and Numerical Implementation
231(2)
11.2.2 Properties of the Binomial Model
233(1)
11.2.3 Verifying Model Assumptions
233(1)
11.2.4 Logistic Regression with Multiple Classes
234(1)
11.3 Classification by Linear Regression
235(1)
11.4 Partial Least Squares Regression
236(3)
11.5 Example: Linear Models for MAGIC Telescope Data
239(8)
11.6 Choosing a Linear Classifier for Your Analysis
247(1)
11.7 Exercises
247(4)
References
248(3)
12 Neural Networks
251(14)
12.1 Perceptrons
251(3)
12.2 The Feed-Forward Neural Network
254(2)
12.3 Backpropagation
256(4)
12.4 Bayes Neural Networks
260(2)
12.5 Genetic Algorithms
262(1)
12.6 Exercises
263(2)
References
263(2)
13 Local Learning and Kernel Expansion
265(42)
13.1 From Input Variables to the Feature Space
266(4)
13.1.1 Kernel Regression
269(1)
13.2 Regularization
270(8)
13.2.1 Kernel Ridge Regression
274(4)
13.3 Making and Choosing Kernels
278(1)
13.4 Radial Basis Functions
279(4)
13.4.1 Example: RBF Classification for the MAGIC Telescope Data
280(3)
13.5 Support Vector Machines (SVM)
283(10)
13.5.1 SVM with Weighted Data
286(2)
13.5.2 SVM with Probabilistic Outputs
288(1)
13.5.3 Numerical Implementation
288(5)
13.5.4 Multiclass Extensions
293(1)
13.6 Empirical Local Methods
293(9)
13.6.1 Classification by Probability Density Estimation
294(1)
13.6.2 Locally Weighted Regression
295(3)
13.6.3 Nearest Neighbors and Fuzzy Rules
298(4)
13.7 Kernel Methods: The Good, the Bad and the Curse of Dimensionality
302(1)
13.8 Exercises
303(4)
References
304(3)
14 Decision Trees
307(24)
14.1 Growing Trees
308(4)
14.2 Predicting by Decision Trees
312(1)
14.3 Stopping Rules
312(1)
14.4 Pruning Trees
313(6)
14.4.1 Example: Pruning a Classification Tree
317(2)
14.5 Trees for Multiple Classes
319(1)
14.6 Splits on Categorical Variables
320(1)
14.7 Surrogate Splits
321(2)
14.8 Missing Values
323(1)
14.9 Variable importance
324(3)
14.10 Why Are Decision Trees Good (or Bad)?
327(1)
14.11 Exercises
328(3)
References
329(2)
15 Ensemble Learning
331(40)
15.1 Boosting
332(26)
15.1.1 Early Boosting
332(1)
15.1.2 AdaBoost for Two Classes
333(3)
15.1.3 Minimizing Convex Loss by Stagewise Additive Modeling
336(7)
15.1.4 Maximizing the Minimal Margin
343(8)
15.1.5 Nonconvex Loss and Robust Boosting
351(6)
15.1.6 Boosting for Multiple Classes
357(1)
15.2 Diversifying the Weak Learner: Bagging, Random Subspace and Random Forest
358(7)
15.2.1 Measures of Diversity
359(2)
15.2.2 Bagging and Random Forest
361(2)
15.2.3 Random Subspace
363(1)
15.2.4 Example: K/π Separation for BaBar PID
364(1)
15.3 Choosing an Ensemble for Your Analysis
365(2)
15.4 Exercises
367(4)
References
367(4)
16 Reducing Multiclass to Binary
371(10)
16.1 Encoding
372(3)
16.2 Decoding
375(3)
16.3 Summary: Choosing the Right Design
378(3)
References
379(2)
17 How to Choose the Right classifier for Your Analysis and Apply It Correctly
381(4)
17.1 Predictive Performance and Interpretability
381(1)
17.2 Matching Classifiers and Variables
382(1)
17.3 Using Classifier Predictions
382(1)
17.4 Optimizing Accuracy
383(1)
17.5 CPU and Memory Requirements
383(2)
18 Methods for Variable Ranking and Selection
385(32)
18.1 Definitions
386(3)
18.1.1 Variable Ranking and Selection
386(1)
18.1.2 Strong and Weak Relevance
386(3)
18.2 Variable Ranking
389(12)
18.2.1 Filters: Correlation and Mutual Information
390(4)
18.2.2 Wrappers: Sequential Forward Selection (SFS), Sequential Backward Elimination (SBE), and Feature-based Sensitivity of Posterior Probabilities (FSPP)
394(6)
18.2.3 Embedded Methods: Estimation of Variable Importance by Decision Trees, Neural Networks, Nearest Neighbors, and Linear Models
400(1)
18.3 Variable Selection
401(12)
18.3.1 Optimal-Set Search Strategies
401(2)
18.3.2 Multiple Testing: Backward Elimination by change in Margin (BECM)
403(7)
18.3.3 Estimation of the Reference Distribution by Permutations: Artificial Contrasts with Ensembles (ACE) Algorithm
410(3)
18.4 Exercises
413(4)
References
414(3)
19 Bump Hunting in Multivariate Data
417(8)
19.1 Voronoi Tessellation and SLEUTH Algorithm
418(2)
19.2 Identifying Box Regions by PRIM and Other Algorithms
420(2)
19.3 Bump Hunting Through Supervised Learning
422(3)
References
423(2)
20 Software Packages for Machine Learning
425(6)
20.1 Tools Developed in HEP
425(1)
20.2 R
426(1)
20.3 Matlab
427(1)
20.4 Tools for Java and Python
428(1)
20.5 What Software Tool Is Right for You?
429(2)
References
430(1)
Appendix A Optimization Algorithms
431(4)
A.1 Line Search
431(1)
A.2 Linear Programming (LP)
432(3)
Index 435
The authors are experts in the use of statistics in particle physics data analysis. Frank C. Porter is Professor at Physics at the California Institute of Technology and has lectured extensively at CalTech, the SLAC Laboratory at Stanford, and elsewhere. Ilya Narsky is Senior Matlab Developer at The MathWorks, a leading developer of technical computing software for engineers and scientists, and the initiator of the StatPatternRecognition, a C++ package for statistical analysis of HEP data. Together, they have taught courses for graduate students and postdocs.
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