1st Edition
Entropy Randomization in Machine Learning
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.
Preface
1. General Concept of Machine Learning
2. Data Sources and Models Chapter
3. Dimension Reduction Methods
4. Randomized Parametric Models
5. Entropy-robust Estimation Procedures for Randomized Models and Measurement Noises
6. Entropy-Robust Estimation Methods for Probabilities of Belonging in Machine Learning Procedures
7. Computational Methods od Randomized Machine Learning
8. Generation Methods for Random Vectors with Given Probability Density Functions over Compact Sets
9. Information Technologies of Randomized Machine Learning
10. Entropy Classification
11. Randomized Machine Learning in Problems of Dynamic Regression and Prediction
Appendix A: Maximum Entropy Estimate (MEE) and Its Asymptotic Efficiency
Appendix B: Approximate Estimation of Structural Characteristics of Linear Dynamic Regression Model (LDR)
Bibliography
Biography
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.
