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Entropy Randomization in Machine Learning [Hardback]

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  • Formāts: Hardback, 392 pages, height x width: 234x156 mm, weight: 716 g, 17 Tables, black and white; 159 Line drawings, black and white; 159 Illustrations, black and white
  • Sērija : Chapman & Hall/CRC Machine Learning & Pattern Recognition
  • Izdošanas datums: 09-Aug-2022
  • Izdevniecība: Chapman & Hall/CRC
  • ISBN-10: 1032306289
  • ISBN-13: 9781032306285
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Entropy Randomization in Machine LearningPalielināt
  • Formāts: Hardback, 392 pages, height x width: 234x156 mm, weight: 716 g, 17 Tables, black and white; 159 Line drawings, black and white; 159 Illustrations, black and white
  • Sērija : Chapman & Hall/CRC Machine Learning & Pattern Recognition
  • Izdošanas datums: 09-Aug-2022
  • Izdevniecība: Chapman & Hall/CRC
  • ISBN-10: 1032306289
  • ISBN-13: 9781032306285
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9781032306285.html
Keywords:
"Entropy Randomization in Machine Learning presents a new approach to machine learning - entropy randomization - to obtain optimal solutions under uncertainty (uncertain data and models of the objects under study). Randomized machine learning procedures involve models with random parameters and maximum entropy estimates of the probability density functions of the model parameters under balance conditions with measured data. Optimality conditions are derived in the form of nonlinear equations with integral components. A new numerical random search method is developed for solving these equations in a probabilistic sense. Along with the theoretical foundations of randomized machine learning, the book considers several applications to binary classification, modelling the dynamics of the Earth population, predicting seasonal electric load fluctuations of power supply systems, and forecasting the area of thermokarst lakes in Western Siberia. This book will appeal to undergraduates and postgraduates specializing in artificial intelligence and machine learning, researchers and engineers involved in the development of applied machine learning systems, and researchers of forecasting problems in various fields"--

Entropy Randomization in Machine Learning presents a new approach to machine learning—entropy randomization—to obtain optimal solutions under uncertainty (uncertain data and models of the objects under study). Randomized machine-learning procedures involve models with random parameters and maximum entropy estimates of the probability density functions of the model parameters under balance conditions with measured data. Optimality conditions are derived in the form of nonlinear equations with integral components. A new numerical random search method is developed for solving these equations in a probabilistic sense. Along with the theoretical foundations of randomized machine learning, Entropy Randomization in Machine Learning considers several applications to binary classification, modelling the dynamics of the Earth’s population, predicting seasonal electric load fluctuations of power supply systems, and forecasting the thermokarst lakes area in Western Siberia.

Features

• A systematic presentation of the randomized machine-learning problem: from data processing, through structuring randomized models and algorithmic procedure, to the solution of applications-relevant problems in different fields

• Provides new numerical methods for random global optimization and computation of multidimensional integrals

• A universal algorithm for randomized machine learning

This book will appeal to undergraduates and postgraduates specializing in artificial intelligence and machine learning, researchers and engineers involved in the development of applied machine learning systems, and researchers of forecasting problems in various fields.



Entropy Randomization in Machine Learning presents a new approach to machine learning - entropy randomization - to obtain optimal solutions under uncertainty (uncertain data and models of the objects under study). 

Preface xiii
Chapter 1 General Concept Of Machine Learning
1(16)
1.1 Transformation Of Knowledge Into Decisions
2(4)
1.2 Structure Of Machine Learning Procedure
6(3)
1.3 Main Concepts Of Machine Learning Procedure
9(3)
1.4 Principles Of Randomized Machine Learning Procedure
12(5)
Chapter 2 Data Sources and Models
17(48)
2.1 Analog Source of Data
18(11)
2.1.1 Deterministic functions
18(3)
2.1.2 Random functions
21(8)
2.2 Digital Source of Data
29(11)
2.2.1 Amplitude and time quantization
30(2)
2.2.2 Audio data
32(3)
2.2.3 Graphical data
35(1)
2.2.4 Text data
36(2)
2.2.5 Government statistical data
38(2)
2.3 Restoration Methods For Missing Data
40(25)
2.3.1 Interpolation
40(3)
2.3.2 Auxiliary dynamic models
43(2)
2.3.3 Spatial entropy decomposition
45(7)
2.3.4 Randomized restoration method for missing data
52(13)
Chapter 3 Dimension Reduction Methods
65(48)
3.1 Review of Dimension Reduction Methods
65(10)
3.1.1 Singular decomposition method for data matrix
66(2)
3.1.2 Principal component analysis
68(2)
3.1.3 Random projection method
70(3)
3.1.4 Direct and inverse projection
73(2)
3.2 Entropy Optimization Of Sequential Procedure
75(6)
3.2.1 Optimality conditions and algorithm
75(2)
3.2.2 Approximation of information cross-entropy functional
77(4)
3.3 Entropy Optimization Of Parallel Procedure
81(3)
3.3.1 Definition and structure
81(1)
3.3.2 Optimality conditions and algorithm
81(3)
3.4 Entropy Reduction Under Matrix Norm And Information Capacity Constraints
84(3)
3.5 Estimating Efficiency Of Dimension Reduction For Linear Model Learning
87(5)
3.5.1 Linear model
88(1)
3.5.2 Comparing s- and r-problems of RML
89(3)
3.6 Estimating Efficiency Of Edr For Binary Classification Problems
92(8)
3.6.1 Linear classifier
92(1)
3.6.2 Scheme of computational experiment
93(1)
3.6.3 Results of experiment
94(6)
3.7 Entropy Methods For Random Projection
100(13)
3.7.1 Statements of Entropy Randomized Projection Problems
100(3)
3.7.2 Algorithms for Entropy Randomized Projection
103(3)
3.7.3 Implementation of random projectors and their numerical characteristics
106(1)
3.7.4 Random projector matrices with given values of elements
107(3)
3.7.5 Choice of appropriate projector matrix from Q (3.138)
110(3)
Chapter 4 Randomized Parametric Models
113(44)
4.1 Definition, Characteristics And Classification
113(3)
4.2 "Single Input--Ensemble Output" Randomized Parametric Model
116(24)
4.2.1 Static models
116(4)
4.2.2 Functional description of dynamic models
120(1)
4.2.3 Linear dynamic models
120(5)
4.2.4 Nonlinear dynamic models with power nonlinearities
125(8)
4.2.5 Nonlinear dynamic models with polynomial nonlinearities
133(4)
4.2.6 Randomized neural networks
137(3)
4.3 "(Single Input, Feedback)--Ensemble Output": Dynamic Randomized Parametric Model
140(8)
4.3.1 Definition and structure
140(2)
4.3.2 Linear dynamic models
142(2)
4.3.3 Nonlinear dynamic models with power nonlinearities
144(3)
4.3.4 Nonlinear dynamic models with polynomial nonlinearities
147(1)
4.4 Probabilistic Characteristics Of Randomized Parameters And Ensembles
148(9)
Chapter 5 Entropy-Robust Estimation Procedures
157(26)
5.1 Structure Of Entropy-Robust Estimation Procedure
158(8)
5.2 Entropy-Robust Estimation Algorithms For Probability Density Functions
166(5)
5.2.1 Estimation algorithms for RPM-Orig model
166(2)
5.2.2 Estimation algorithms for RPM-Rel model
168(1)
5.2.3 Estimation algorithms for RPM-F model with measurement errors of input and output
169(2)
5.3 Optimality Conditions For Lyapunov-Type Problems
171(2)
5.4 Optimality Conditions And Structure Of Entropy-Optimal Probability Density Functions
173(7)
5.4.1 Randomized models of the RPM-Orig class with output errors
174(3)
5.4.2 Randomized models of the RPM-Rel class with output errors
177(2)
5.4.3 Randomized models of the RPM-Orig class with input and output errors
179(1)
5.5 Equations For Lagrange Multipliers
180(3)
Chapter 6 Entropy-Robust Estimation Methods
183(14)
6.1 Entropy-Robust Estimation Algorithms For Probabilities Of Belonging
184(4)
6.1.1 ML algorithm for RPM-QuaRand model with normalized probabilities of belonging
185(2)
6.1.2 ML algorithm for RPM-QuaRand model with interval-type probabilities of belonging
187(1)
6.2 Functional Description Of Dynamic Rpm-Quarand Models
188(3)
6.3 Optimality Conditions And Structure Of Entropy-Optimal Probabilities Of Belonging
191(6)
Chapter 7 Computational Methods Of Randomized Machine Learning
197(40)
7.1 Classes Of Balance Equations In Rml And Ml Procedures
198(4)
7.2 Monte Carlo Packet Iterations For Global Optimization
202(21)
7.2.1 Canonical form of global optimization problem
203(2)
7.2.2 Idea of method and concept of solution
205(1)
7.2.3 Probabilistic characteristics of random sequences F and U
206(3)
7.2.4 Convergence of GFS algorithm
209(2)
7.2.5 Study of decrements sequence U
211(2)
7.2.6 Admissible set K(z) of general form
213(2)
7.2.7 Logical structure of GFS algorithm
215(2)
7.2.8 Experimental study of GFS algorithm
217(6)
7.3 On Calculation Of Multidimensional Integrals Using Monte Carlo Method
223(7)
7.4 Multiplicative Algorithms With P-Active Variables
230(7)
Chapter 8 Generation Methods
237(12)
8.1 A Survey Of Generation Methods For Random Objects
238(3)
8.1.1 Random variables
238(2)
8.1.2 Random vectors
240(1)
8.2 Direct Generation Method For Random Vectors With Given Probability Density Function
241(3)
8.2.1 Unit cube Q
241(1)
8.2.2 Compact set Q
242(2)
8.3 Approximation Of Given Probability Density Function
244(5)
Chapter 9 Information Technologies Of Randomized Machine Learning
249(18)
9.1 Architecture Of Modern Computer Systems
250(5)
9.2 Universal Multithreaded Architecture
255(3)
9.3 Information Technologies Of Randomized Machine Learning
258(6)
9.4 Implementation Of Packet Iterations
264(3)
Chapter 10 Entropy Classification
267(18)
10.1 Standard Classification Methods
267(6)
10.1.1 Decision Tree
268(1)
10.1.2 k-Nearest Neighbor
269(1)
10.1.3 Naive Bayes
270(1)
10.1.4 Linear classifiers
271(2)
10.2 Composition Algorithms
273(2)
10.2.1 Bagging
274(1)
10.2.2 Stacking
274(1)
10.2.3 Boosting
275(1)
10.3 Entropy Classification
275(10)
10.3.1 Problem formulation
275(1)
10.3.2 Learning stage
276(2)
10.3.3 Testing stage
278(2)
10.3.4 Numerical examples
280(5)
Chapter 11 Problems Of Dynamic Regression
285(48)
11.1 Restoration Of Dynamic Relationships In Applications
286(1)
11.2 Randomized Model Of World Population Dynamics
286(8)
11.2.1 RML procedure for learning of World Population Dynamics Model
289(1)
11.2.2 Numerical results
290(4)
11.3 Randomized Forecasting Of Daily Electrical Load In Power System
294(15)
11.3.1 Electrical Load Model
295(1)
11.3.2 Learning dataset
296(3)
11.3.3 Entropy-optimal probability density functions of parameters and noises
299(2)
11.3.4 Results of model learning
301(3)
11.3.5 Model testing
304(1)
11.3.6 Randomized prediction of AT-daily load
305(4)
11.4 Entropy Randomized Modelling And Forecasting Of Thermokarst Lake Area Evolution In Western Siberia
309(24)
11.4.1 Thermokarst lakes and climate change
309(1)
11.4.2 Thermokarst lakes of Western Siberia, tools and problems of their study
309(2)
11.4.3 Structures of randomized models of thermokarst lakes state
311(3)
11.4.4 Data on the state of thermokarst lakes
314(3)
11.4.5 Entropy-Randomized machine learning of LDRR
317(1)
11.4.5.1 Formation of data sets to train LDRR
317(1)
11.4.5.2 ERML algorithm
318(3)
11.4.6 Testing procedure, data and accuracy estimates
321(3)
11.4.7 Randomized forecasting of thermokarst lakes area evolution
324(1)
11.4.8 Results of training, testing and forecasting the temporal evolution of thermokarst lakes area in Western Siberia
324(1)
11.4.8.1 Randomized training (1973--1997)
324(3)
11.4.8.2 Testing (1998--2007)
327(1)
11.4.8.3 Randomized forecasting (2008--2023)
328(5)
Appendix A MAXIMUM ENTROPY ESTIMATE (MEE) AND ITS ASYMPTOTIC EFFICIENCY
333(10)
A.1 Statement Of Maximum Entropy Estimation Problem
333(2)
A.2 Existence of Implicit Function θ(Y(R), X(R))
335(4)
A.3 Asymptotic Efficiency of Maximum Entropy Estimates
339(4)
Appendix B APPROXIMATE ESTIMATION OF LDR
343(4)
B.1 Order P
344(1)
B.2 Parameters Ranges
344(3)
Bibliography 347(18)
Index 365
Yuri S. Popkov: Doctor of Engineering, Professor, Academician of Russian Academy of Sciences; Chief Researcher at Federal Research Center Computer Science and Control, Russian Academy of Sciences; Chief Researcher at Trapeznikov Institute of Control Sciences, Russian Academy of Sciences; Professor at Lomonosov Moscow State University. Author of more than 250 scientific publications, including 15 monographs. His research interests include stochastic dynamic systems, optimization, machine learning, and macrosystem modeling.

Alexey Yu. Popkov: Candidate of Sciences, Leading Researcher at Federal Research Center Computer Science and Control, Russian Academy of Sciences; author of 47 scientific publications. His research interests include software engineering, high-performance computing, data mining, machine learning, and entropy methods.

Yuri A. Dubnov: MSc in Physics, Researcher at Federal Research Center Computer Science and Control, Russian Academy of Sciences. Author of more than 18 scientific publications. His research interests include machine learning, forecasting, randomized approaches, and Bayesian estimation.