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Table of Contents
Preface; Contents; Introduction; Basic Notations; Part I Randomized Algorithms; 1Feedback, Averaging and Randomization in Control and Data Mining; 1.1Feedback; 1.1.1Information and Control; 1.1.2Signals and Data Sizes; 1.1.3Observations with Noise; 1.2Averaging; 1.2.1Data Averaging ; 1.2.2Averaging in Stochastic Control; 1.3Efficiency of Closed-Loop Strategies under Uncertainty; 1.4Estimation under Arbitrary Noise; 1.4.1Can Smart Estimates Be Obtained?; 1.4.2Randomized and Bayesian Approaches; 1.5Randomization for Reducing Computational Complexity ; 1.6Quantum Computing; 2Historical Overview
2.1Game Theory2.2Monte Carlo Method, Random Search; 2.2.1Random Search, Simulating Annealing, Genetic Algorithms; 2.2.2Probabilistic Methods in a Control Syntheses; 2.3Estimation and Filtering under Arbitrary External Noises; 2.3.1Randomized Stochastic Approximation; 2.3.2Linear Regression and Filtering; 2.3.3Compressive Sensing; 2.3.4Randomized Control Strategies; 2.4Data Mining and Machine Learning; 2.4.1Clustering; 2.4.2Cluster Validation; Part II Randomization in Estimation, Identification and Filtering Problems; 3Randomized Stochastic Approximation; 3.1 Mean-Risk Optimization
3.2Exciting Testing Perturbation as Randomization3.3Convergence of Estimates; 3.4Fastest Rate of Convergence; 3.5Tracking; 3.6Algorithm Implementation and Quantum Computing; 3.7Applications; 3.7.1Optimization of a Server Processing Queue; 3.7.2Load Balancing; 3.7.3UAV Soaring; 4Linear Models; 4.1Linear Regression and Filtering under Arbitrary External Noise; 4.1.1Linear Regression; 4.1.2Application in Photoemission Experiments; 4.1.3Moving Average; 4.1.4Filtering; 4.2Random Projections and Sparsity; 4.2.1Compressed (Spars) Signals; 4.2.2Transforming Coding; 4.2.3Compressive Sensing
4.2.4Universal Measurement Matrix: Random Projections4.2.5Reconstruction Algorithms through 1-Optimization and Others; 4.2.6Some Applications; 5Randomized Control Strategies; 5.1Preliminary Example; 5.2Problem Statement; 5.3Control Actions with Randomized Test Signals; 5.4Assumptions and Model Reparameterization; 5.5Stochastic Approximation Algorithm; 5.6Procedure for Constructing Confidence Regions; 5.7Combined Procedure; 5.8Randomized Control for Small UAV under Unknown Arbitrary Wind Disturbances; Part III Data Mining; 6Clustering; 6.1Partition into k Clusters; 6.2k-Means Clustering
6.2.1Randomized Iterative k-Means6.2.2Example; 6.3Clustering and Compressive Sensing; 6.4Gaussian Mixtures and Clustering; 6.5Information Methods; 6.5.1Mixture Clustering Model
An Information Standpoint; 6.5.2Information Bottleneck; 6.6Spectral Clustering; 6.6.1The Ng-Jordan-Weiss (NJW) Algorithm; 6.6.2sigma-Learning and Model Selection; 6.6.3Numerical Experiments; 6.6.4Application to Writing Style Determination; 7Cluster Validation ; 7.1Stability Criteria; 7.1.1External Indexes; 7.1.2The Clest Algorithm; 7.1.3The General Stability Approach; 7.2Geometrical Criteria; 7.3Information Criteria
2.1Game Theory2.2Monte Carlo Method, Random Search; 2.2.1Random Search, Simulating Annealing, Genetic Algorithms; 2.2.2Probabilistic Methods in a Control Syntheses; 2.3Estimation and Filtering under Arbitrary External Noises; 2.3.1Randomized Stochastic Approximation; 2.3.2Linear Regression and Filtering; 2.3.3Compressive Sensing; 2.3.4Randomized Control Strategies; 2.4Data Mining and Machine Learning; 2.4.1Clustering; 2.4.2Cluster Validation; Part II Randomization in Estimation, Identification and Filtering Problems; 3Randomized Stochastic Approximation; 3.1 Mean-Risk Optimization
3.2Exciting Testing Perturbation as Randomization3.3Convergence of Estimates; 3.4Fastest Rate of Convergence; 3.5Tracking; 3.6Algorithm Implementation and Quantum Computing; 3.7Applications; 3.7.1Optimization of a Server Processing Queue; 3.7.2Load Balancing; 3.7.3UAV Soaring; 4Linear Models; 4.1Linear Regression and Filtering under Arbitrary External Noise; 4.1.1Linear Regression; 4.1.2Application in Photoemission Experiments; 4.1.3Moving Average; 4.1.4Filtering; 4.2Random Projections and Sparsity; 4.2.1Compressed (Spars) Signals; 4.2.2Transforming Coding; 4.2.3Compressive Sensing
4.2.4Universal Measurement Matrix: Random Projections4.2.5Reconstruction Algorithms through 1-Optimization and Others; 4.2.6Some Applications; 5Randomized Control Strategies; 5.1Preliminary Example; 5.2Problem Statement; 5.3Control Actions with Randomized Test Signals; 5.4Assumptions and Model Reparameterization; 5.5Stochastic Approximation Algorithm; 5.6Procedure for Constructing Confidence Regions; 5.7Combined Procedure; 5.8Randomized Control for Small UAV under Unknown Arbitrary Wind Disturbances; Part III Data Mining; 6Clustering; 6.1Partition into k Clusters; 6.2k-Means Clustering
6.2.1Randomized Iterative k-Means6.2.2Example; 6.3Clustering and Compressive Sensing; 6.4Gaussian Mixtures and Clustering; 6.5Information Methods; 6.5.1Mixture Clustering Model
An Information Standpoint; 6.5.2Information Bottleneck; 6.6Spectral Clustering; 6.6.1The Ng-Jordan-Weiss (NJW) Algorithm; 6.6.2sigma-Learning and Model Selection; 6.6.3Numerical Experiments; 6.6.4Application to Writing Style Determination; 7Cluster Validation ; 7.1Stability Criteria; 7.1.1External Indexes; 7.1.2The Clest Algorithm; 7.1.3The General Stability Approach; 7.2Geometrical Criteria; 7.3Information Criteria