Swarm intelligence methods for statistical regression

✍ Scribed by Mohanty Soumya D

• Publisher: CRC Press
• Year: 2019
• Tongue: English
• Leaves: 137
• Category: Library

✦ Synopsis

Introduction -- Stochastic optimization theory -- Evolutionary computation and swarm -- Particle swarm optimization -- PSO applications.;"A core task in Big Data analytics is the fitting of flexible, high-dimensional, models to noisy data in order to capture meaningful patterns. This can often result in challenging non-linear and non-convex global optimization problems. The large data volume that must be handled in Big Data applications further increases the difficulty of this problem. This book will describe methods from the field of computational swarm intelligence (SI) and how they can be used to solve optimization problems encountered in Big Data analytics. It will consider some generic data analysis problems, and how they may be addressed using SI methods"--

✦ Table of Contents

Cover......Page 1
Half Title......Page 2
Title Page......Page 4
Copyright Page......Page 5
Dedication......Page 6
Table of Contents......Page 8
Preface......Page 12
Conventions and Notation......Page 16
1.1 OPTIMIZATION IN STATISTICAL ANALYSIS......Page 18
1.2 STATISTICAL ANALYSIS: BRIEF OVERVIEW......Page 20
1.3.1 Parametric regression......Page 23
1.3.2 Non-parametric regression......Page 25
1.4 HYPOTHESES TESTING......Page 28
1.5.1 Noise in the independent variable......Page 32
1.5.2 Statistical analysis and machine learning......Page 33
CHAPTER 2: Stochastic Optimization Theory......Page 36
2.1 TERMINOLOGY......Page 37
2.2 CONVEX AND NON-CONVEX OPTIMIZATION PROBLEMS......Page 38
2.3 STOCHASTIC OPTIMIZATION......Page 41
2.4 EXPLORATION AND EXPLOITATION......Page 45
2.5 BENCHMARKING......Page 47
2.6 TUNING......Page 49
2.7 BMR STRATEGY......Page 51
2.8 PSEUDO-RANDOM NUMBERS AND STOCHASTIC OPTIMIZATION......Page 52
2.9 NOTES......Page 53
3.1 OVERVIEW......Page 54
3.2 EVOLUTIONARY COMPUTATION......Page 56
3.3 SWARM INTELLIGENCE......Page 58
3.4 NOTES......Page 59
CHAPTER 4: Particle Swarm Optimization......Page 62
4.1 KINEMATICS: GLOBAL-BEST PSO......Page 63
4.2 DYNAMICS: GLOBAL-BEST PSO......Page 65
4.2.2 Interpreting the velocity update rule......Page 66
4.2.3 Importance of limiting particle velocity......Page 68
4.2.4 Importance of proper randomization......Page 70
4.2.5 Role of inertia......Page 71
4.3 KINEMATICS: LOCAL-BEST PSO......Page 73
4.4 DYNAMICS: LOCAL-BEST PSO......Page 75
4.5 STANDARDIZED COORDINATES......Page 76
4.7 NOTES......Page 77
4.7.1 Additional PSO variants......Page 78
4.7.2 Performance example......Page 80
CHAPTER 5: PSO Applications......Page 82
5.1.1 Fitness function......Page 83
5.1.2 Data simulation......Page 84
5.1.3 Parametric degeneracy and noise......Page 85
5.2.1 Tuning......Page 87
5.2.2 Results......Page 91
5.3 NON-PARAMETRIC REGRESSION......Page 94
5.3.1 Reparametrization in regression spline......Page 95
5.3.2 Results: Fixed number of breakpoints......Page 98
5.3.3 Results: Variable number of breakpoints......Page 99
5.4 NOTES AND SUMMARY......Page 101
5.4.1 Summary......Page 104
A.1 RANDOM VARIABLE......Page 106
A.2 PROBABILITY MEASURE......Page 107
A.3 JOINT PROBABILITY......Page 109
A.4 CONTINUOUS RANDOM VARIABLES......Page 111
A.5 EXPECTATION......Page 114
A.6 COMMON PROBABILITY DENSITY FUNCTIONS......Page 115
B.1 DEFINITION......Page 118
B.2 B-SPLINE BASIS......Page 120
APPENDIX C: Analytical Minimization......Page 124
C.1 QUADRATIC CHIRP......Page 125
C.2 SPLINE-BASED SMOOTHING......Page 126
Bibliography......Page 128
Index......Page 134

✦ Subjects

Big data;Computational intelligence;COMPUTERS / Databases / Data Warehousing;Regression analysis;Swarm intelligence;Electronic books