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written by Aharon Ben-Tal Laurent El Ghaoui Arkadi Nemirovski Copyright © 2009 by Princeton University Press PART I. ROBUST LINEAR OPTIMIZATION 1 Chapter 1. Uncertain Linear Optimization Problems and their Robust Counterparts 3 1.1 Data Uncertainty in Linear Optimization 3 1.2 Uncertain Linear Problems and their Robust Counterparts 7 1.3 Tractability of Robust Counterparts 16 1.4 Non-Affine Perturbations 23 1.5 Exercises 25 1.6 Notes and Remarks 25 Chapter 2. Robust Counterpart Approximations of Scalar Chance Constraints 27 2.1 How to Specify an Uncertainty Set 27 2.2 Chance Constraints and their Safe Tractable Approximations 28 2.3 Safe Tractable Approximations of Scalar Chance Constraints: Basic Examples 31 2.4 Extensions 44 2.5 Exercises 60 2.6 Notes and Remarks 64 Chapter 3. Globalized Robust Counterparts of Uncertain LO Problems 67 3.1 Globalized Robust Counterpart — Motivation and Definition 67 3.2 Computational Tractability of GRC 69 3.3 Example: Synthesis of Antenna Arrays 70 3.4 Exercises 79 3.5 Notes and Remarks 79 Chapter 4. More on Safe Tractable Approximations of Scalar Chance Constraints 81 4.1 Robust Counterpart Representation of a Safe Convex Approximation to a Scalar Chance Constraint 81 4.2 Bernstein Approximation of a Chance Constraint 83 4.3 From Bernstein Approximation to Conditional Value at Risk and Back 90 4.4 Majorization 105 4.5 Beyond the Case of Independent Linear Perturbations 109 4.6 Exercises 136 4.7 Notes and Remarks 145 PART II. ROBUST CONIC OPTIMIZATION 147 Chapter 5. Uncertain Conic Optimization: The Concepts 149 5.1 Uncertain Conic Optimization: Preliminaries 149 5.2 Robust Counterpart of Uncertain Conic Problem: Tractability 151 5.3 Safe Tractable Approximations of RCs of Uncertain Conic Inequalities 153 5.4 Exercises 156 5.5 Notes and Remarks 157 Chapter 6. Uncertain Conic Quadratic Problems with Tractable RCs 159 6.1 A Generic Solvable Case: Scenario Uncertainty 159 6.2 Solvable Case I: Simple Interval Uncertainty 160 6.3 Solv

2016 Deep Learning by MIT Press: Abstracts: 1 Introduction Part I: Applied Math and Machine Learning Basics 2 Linear Algebra 3 Probability and Information Theory 4 Numerical Computation 5 Machine Learning Basics Part II: Modern Practical Deep Networks 6 Deep Feedforward Networks 7 Regularization for Deep Learning 8 Optimization for Training Deep Models 9 Convolutional Networks 10 Sequence Modeling: Recurrent and Recursive Nets 11 Practical Methodology 12 Applications Part III: Deep Learning Research 13 Linear Factor Models 14 Autoencoders 15 Representation Learning 16 Structured Probabilistic Models for Deep Learning 17 Monte Carlo Methods 18 Confronting the Partition Function 19 Approximate Inference 20 Deep Generative Models

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此m文件返回有用的残差缩放，即预测误差平方和（PRESS）。 要计算 PRESS，请选择一个观察值 i。 将回归模型拟合到剩余的 n-1 个观测值，并使用此方程来预测保留的观测值 y_i。 用 ye_(i) 表示这个预测值，我们可以找到点 i 的预测误差为 e_(i)=y_i - ye_(i)。 预测误差通常称为第 i 个 PRESS 残差。 对于每个观测值 i = 1,2,...,n 重复此过程，生成一组 n 个 PRESS 残差 e_(1),e_(2),...,e_(n)。 然后将 PRESS 统计量定义为 n 个 PRESS 残差的平方和，如下所示， PRESS = i_Sum_n e_(i)^2 = i_Sum_n [y_i - ye_(i)]^2 因此，PRESS 使用 n-1 个观测的这种可能子集作为估计数据集，并且每个观测依次用于形成预测数据集。 在构建这个 m 文件时

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